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Show all of the details of your work Consider the ordinary differential equation (x2 + 1)...
please answer immediately thank you 4. [-/1 Points] DETAILS SCALCCC4 7.1.006. Consider the following differential equation....
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4. [-/1 Points] DETAILS SCALCCC4 7.1.006. Consider the following differential equation. ry + y = 5 (a) Show that every member of the family of functions y = (51n(x) + C)/x is a solution of the differential equation. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Illustrate part (a) by graphing several members of the family of solutions on a common screen. (Do this on paper. Your instructor...
Find two power series solutions of the given differential equation about the ordinary point x =...
Find two power series solutions of the given differential
equation about the ordinary point x = 0. y′′ − 4xy′ + y = 0
Find two power series solutions of the given differential equation about the ordinary point x = 0. y!' - 4xy' + y = 0 Step 1 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" - 4xy' + y = 0 By Theorem 6.2.1, we know two...
x² + * Full workings requined. For x 20 consider the ordinary differential equation de 2x²+4²...
x² + * Full workings requined. For x 20 consider the ordinary differential equation de 2x²+4² - xy 1) find the solution of this differential equation that satisfies the condition that y=2 have the answer in the implicit fam G(x,y)=0. for some function a which you can find. x=2
P3.* Consider the ordinary differential equation: u” + 1 = 0. a) Show that this equation...
P3.* Consider the ordinary differential equation: u” + 1 = 0. a) Show that this equation together with the boundary conditions u(0) = 2, u(a) = 0 has no solution. b) Show that this equation together with the boundary conditions u(0) = 2, u(a) = –2 has infinitely many solutions.
Write a Maple program to solve analytically the ordinary differential equation dy dt = y 2...
Write a Maple program to solve analytically the ordinary differential equation dy dt = y 2 + 1 with initial condition y(0) = 0. What solution is found? Verify (on paper) that the solution found satisfies the differential equation and initial condition.
15. [-75 Points] DETAILS LARCALCET7 5.8.061.MI. Find the particular solution of the differential equation that satisfies...
15. [-75 Points] DETAILS LARCALCET7 5.8.061.MI. Find the particular solution of the differential equation that satisfies the initial condition. 1 dy dx = y(0) = 21 y =
1) Find the particular solution of the differential equation that satisfies the initial condition...
1) Find the particular solution of the differential equation that satisfies the initial condition. (Enter your solution as an equation.) Differential Equation Initial Condition yy' − 4ex = 0 y(0) = 9 2) Find the particular solution of the differential equation that satisfies the initial condition. (Enter your solution as an equation.) Differential Equation Initial Condition 10xy' − ln(x5) = 0, x > 0 y(1) = 21 Just really confused on how to do these, hope someone can help! :)
plz show work, thank you 1. For the following problem, determine if the following equations are...
plz show work, thank you
1. For the following problem, determine if the following equations are linear or nonlinear. If it is linear, classify it as being homogeneous or non-homogeneous, with constant coefficients or variable coefficient (5 points) y" +(1- x)y'+ xy = sin(x) 2. Consider the differential equation: y" - 4y' +5y = 0 (a) (5 points) Find a general solution to the differential equation (b) (5 points) Find a solution to the differential equation that satisfies the initial...
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72,...
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72, roots of the characteristic polynomial of the equation above. 11,2 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -4, y'(0) = 1. g(t) = M Consider the differential equation y" – 64 +9y=0. (a) Find r1...
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use...
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use Abel's formula to find the Wronskian of any two solutions of this equation and W[y1,y2](t). What do you observe? compare it to = t1 and y2(t) = t-1 nt represent a fundamental set of solu f) (2 points) Determine if y1 (t) tions (2 points) Find the general solution of t2y" +3ty' +y = 0. g) Solve the initial value problem t2y" + 3ty/...
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4. [-/1 Points] DETAILS SCALCCC4 7.1.006. Consider the following differential equation. ry + y = 5 (a) Show that every member of the family of functions y = (51n(x) + C)/x is a solution of the differential equation. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Illustrate part (a) by graphing several members of the family of solutions on a common screen. (Do this on paper. Your instructor...
Find two power series solutions of the given differential
equation about the ordinary point x = 0. y′′ − 4xy′ + y = 0
Find two power series solutions of the given differential equation about the ordinary point x = 0. y!' - 4xy' + y = 0 Step 1 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" - 4xy' + y = 0 By Theorem 6.2.1, we know two...
x² + * Full workings requined. For x 20 consider the ordinary differential equation de 2x²+4² - xy 1) find the solution of this differential equation that satisfies the condition that y=2 have the answer in the implicit fam G(x,y)=0. for some function a which you can find. x=2
P3.* Consider the ordinary differential equation: u” + 1 = 0. a) Show that this equation together with the boundary conditions u(0) = 2, u(a) = 0 has no solution. b) Show that this equation together with the boundary conditions u(0) = 2, u(a) = –2 has infinitely many solutions.
15. [-75 Points] DETAILS LARCALCET7 5.8.061.MI. Find the particular solution of the differential equation that satisfies the initial condition. 1 dy dx = y(0) = 21 y =
plz show work, thank you
1. For the following problem, determine if the following equations are linear or nonlinear. If it is linear, classify it as being homogeneous or non-homogeneous, with constant coefficients or variable coefficient (5 points) y" +(1- x)y'+ xy = sin(x) 2. Consider the differential equation: y" - 4y' +5y = 0 (a) (5 points) Find a general solution to the differential equation (b) (5 points) Find a solution to the differential equation that satisfies the initial...
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72, roots of the characteristic polynomial of the equation above. 11,2 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -4, y'(0) = 1. g(t) = M Consider the differential equation y" – 64 +9y=0. (a) Find r1...
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use Abel's formula to find the Wronskian of any two solutions of this equation and W[y1,y2](t). What do you observe? compare it to = t1 and y2(t) = t-1 nt represent a fundamental set of solu f) (2 points) Determine if y1 (t) tions (2 points) Find the general solution of t2y" +3ty' +y = 0. g) Solve the initial value problem t2y" + 3ty/...
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