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![sol - Given 2xy + y 74 xzaxy (642xy) dy + (2xy + y +4]dx 2.0 N 2M = 2x+2y 7 Exact ay . J Den 2N = 2x+2y 24 y 20 (Exact D.E] t](http://img.homeworklib.com/questions/15b28690-aca5-11ea-b7c1-e17925930ad6.png?x-oss-process=image/resize,w_560)
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Chapter 2, Miscellaneous Problems, Question 05 Solve the given differential equation. All solutions should be found...
If = Q, where Q is a function of y only, then the differential equation M...
If = Q, where Q is a function of y only, then the differential equation M + Ny = 0 has an integrating factor of the form +(y) = es Q(u) dy Find an integrating factor and solve the given equation. ydx + (3xy - e-39) dy=0 Enclose arguments of functions in parentheses. For example, sin (22) To enter y in text mode, type (ly) or abs(y). Use multiplication sign in all cases of multiplication. The integrating factor is (y)...
MESSAGE M Chapter 3, Section 3.6, Question 05 Find the general solution of the differential equat...
MESSAGE M Chapter 3, Section 3.6, Question 05 Find the general solution of the differential equation + 16-13sec"(40, 0 < t <晋 Use C, C2,... for the constants of integration. Enter an exact answer Enter in lal as In (lal), and do not simplify Equation Editor Common Ω Matrix sin(a)cos(a sec(a) 읊 ffdz).dz tan(a) : 떼 y(t)- arch
MESSAGE M Chapter 3, Section 3.6, Question 05 Find the general solution of the differential equation + 16-13sec"(40, 0
April 13, 2020 MATH2107- MIDTERM EXAM.I/1 Q.1(40 pts) Find the solutions of the following differential equa-...
April 13, 2020 MATH2107- MIDTERM EXAM.I/1 Q.1(40 pts) Find the solutions of the following differential equa- tion W (2xy + 3y?)dx - (2xy + x2)dy = 0. Q.2(60 pts) Given the differential equation (2xy + y)dx + (2y3 – x)dy = 0. (a) Assuming the integration factor of the form u= u(y), de- termine p(y) so as to make the above equation exact. (b) Then, find the solution of the differential equation. Duration of the exam is 40 minutes.
Answer all Please! Thanks 1. Confirming Solutions to Differential Equations: Verify that each function does in fact solve the given differential equation. If there are parameters in the function (A....
Answer all Please! Thanks
1. Confirming Solutions to Differential Equations: Verify that each function does in fact solve the given differential equation. If there are parameters in the function (A. b. k), give the range of values of those parameters for which that function is a solution. The prime indicates differentiation with respect od dr' (b) y" + 4y = 0; y = A sin(kx + φ). (c) y"-4s, + 4y = 0, y = Axe . (d) x2y', +...
Find the Wronskian of two solutions (up to a constant multiple) to the differential equation without...
Find the Wronskian of two solutions (up to a constant multiple) to the differential equation without solving the equation: (1 - 2?)y" - 2xy + 2y = 0 (this is a well-known equation called Legendre's equation. Its solutions are called Legendre functions). Impossible to determine from the given information O where c is a constant 1-22 O ce 1-22 where c is a constant O cln |1 - 22 where c is a constant
il Boundary Value Problems, MESSAGE MY INSTRUCTOR STANDARD VIEW Chapter 5, Section 5.3, Question 05 Determine a lower bound for the radius of convergence of series solutions about each given poi...
il Boundary Value Problems, MESSAGE MY INSTRUCTOR STANDARD VIEW Chapter 5, Section 5.3, Question 05 Determine a lower bound for the radius of convergence of series solutions about each given point Xo for the given differential equation. Enter 00 if the series solutions converge everywhere. Equation Editor Ω Matrix Common sinia secia) sin (a) tania) coia) co a) cos-(a) Equation Editor Equation Editor Common Ω Matrix sinia) secta) scia) =-4 : pmin xo = Equation Editor Ω Matrix Common ina)COa)tania)...
Bonus (Abel's formula) a) Show that if y1 and y2 are solutions to the differential equation...
Bonus (Abel's formula) a) Show that if y1 and y2 are solutions to the differential equation y"p(t)y(t)y 0 where p and q are continuous on an interval I, then the Wronskian of y and y2, W(y1,y2) (t) is given by - Sp(t)dt ce W(y1, y2)(t) where c depends on y and y2 (b) Use Abel's formula to find the Wronskian of two solutions to the differential equation ty"(t 1)y 3y 0 Do not solve the differential equation
Use the method for solving homogeneous equations to solve the following differential equation 5(x2 + y2)...
Use the method for solving homogeneous equations to solve the following differential equation 5(x2 + y2) dx + 2xy dy = 0 Ignoring lost solutions, if any, an implicit solution in the form FXy) = C is W = C where (Type an expression using X andy as the variables.) is an arbitrary constant
Question 14 (12 marks) Consider the following separable differential equation. dy cos(z)(-1) dr (a) Find any...
Question 14 (12 marks) Consider the following separable differential equation. dy cos(z)(-1) dr (a) Find any constant solutions of this differential equation and hence write down the solution with initial value y=- when r=7 (b) Use partial fractions to evaluate 1 dy. 1 (c) Use the method for solving separable differential equations to solve this DE in the case where y 0 when r T. You may assume that the solution does not cross the constant solutions you found in...
Question 4 Solve the differential equation. 2xy' + y = 2V* Question 5 Solve the initial...
Question 4 Solve the differential equation. 2xy' + y = 2V* Question 5 Solve the initial value problem xy' + y = xln x , y(1) = 0 Question 7 Find the derivative. c = tet, g =t+ sin t Question 8 Find the equation of the tangent to the curve at the given point. x = ť – t, y=ť +t+1 ; (0,3)
If = Q, where Q is a function of y only, then the differential equation M + Ny = 0 has an integrating factor of the form +(y) = es Q(u) dy Find an integrating factor and solve the given equation. ydx + (3xy - e-39) dy=0 Enclose arguments of functions in parentheses. For example, sin (22) To enter y in text mode, type (ly) or abs(y). Use multiplication sign in all cases of multiplication. The integrating factor is (y)...
MESSAGE M Chapter 3, Section 3.6, Question 05 Find the general solution of the differential equation + 16-13sec"(40, 0 < t <晋 Use C, C2,... for the constants of integration. Enter an exact answer Enter in lal as In (lal), and do not simplify Equation Editor Common Ω Matrix sin(a)cos(a sec(a) 읊 ffdz).dz tan(a) : 떼 y(t)- arch
MESSAGE M Chapter 3, Section 3.6, Question 05 Find the general solution of the differential equation + 16-13sec"(40, 0
April 13, 2020 MATH2107- MIDTERM EXAM.I/1 Q.1(40 pts) Find the solutions of the following differential equa- tion W (2xy + 3y?)dx - (2xy + x2)dy = 0. Q.2(60 pts) Given the differential equation (2xy + y)dx + (2y3 – x)dy = 0. (a) Assuming the integration factor of the form u= u(y), de- termine p(y) so as to make the above equation exact. (b) Then, find the solution of the differential equation. Duration of the exam is 40 minutes.
Answer all Please! Thanks
1. Confirming Solutions to Differential Equations: Verify that each function does in fact solve the given differential equation. If there are parameters in the function (A. b. k), give the range of values of those parameters for which that function is a solution. The prime indicates differentiation with respect od dr' (b) y" + 4y = 0; y = A sin(kx + φ). (c) y"-4s, + 4y = 0, y = Axe . (d) x2y', +...
Find the Wronskian of two solutions (up to a constant multiple) to the differential equation without solving the equation: (1 - 2?)y" - 2xy + 2y = 0 (this is a well-known equation called Legendre's equation. Its solutions are called Legendre functions). Impossible to determine from the given information O where c is a constant 1-22 O ce 1-22 where c is a constant O cln |1 - 22 where c is a constant
il Boundary Value Problems, MESSAGE MY INSTRUCTOR STANDARD VIEW Chapter 5, Section 5.3, Question 05 Determine a lower bound for the radius of convergence of series solutions about each given point Xo for the given differential equation. Enter 00 if the series solutions converge everywhere. Equation Editor Ω Matrix Common sinia secia) sin (a) tania) coia) co a) cos-(a) Equation Editor Equation Editor Common Ω Matrix sinia) secta) scia) =-4 : pmin xo = Equation Editor Ω Matrix Common ina)COa)tania)...
Bonus (Abel's formula) a) Show that if y1 and y2 are solutions to the differential equation y"p(t)y(t)y 0 where p and q are continuous on an interval I, then the Wronskian of y and y2, W(y1,y2) (t) is given by - Sp(t)dt ce W(y1, y2)(t) where c depends on y and y2 (b) Use Abel's formula to find the Wronskian of two solutions to the differential equation ty"(t 1)y 3y 0 Do not solve the differential equation
Use the method for solving homogeneous equations to solve the following differential equation 5(x2 + y2) dx + 2xy dy = 0 Ignoring lost solutions, if any, an implicit solution in the form FXy) = C is W = C where (Type an expression using X andy as the variables.) is an arbitrary constant
Question 14 (12 marks) Consider the following separable differential equation. dy cos(z)(-1) dr (a) Find any constant solutions of this differential equation and hence write down the solution with initial value y=- when r=7 (b) Use partial fractions to evaluate 1 dy. 1 (c) Use the method for solving separable differential equations to solve this DE in the case where y 0 when r T. You may assume that the solution does not cross the constant solutions you found in...
Question 4 Solve the differential equation. 2xy' + y = 2V* Question 5 Solve the initial value problem xy' + y = xln x , y(1) = 0 Question 7 Find the derivative. c = tet, g =t+ sin t Question 8 Find the equation of the tangent to the curve at the given point. x = ť – t, y=ť +t+1 ; (0,3)
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