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Question 8 Solve. In other words, integrate the right hand side of the equation. y' =...
Daniela tried to solve the differential equation dy d: 9 = 22.e-y. This is her work:...
Daniela tried to solve the differential equation dy d: 9 = 22.e-y. This is her work: 9 = 22. e-y d Step 1: Je="dy= [ 23 dx Step 2: . ev = x² + a Step 3: e-*= -+C Step 4: In(e-y) = ln(-x? + C) Step 5: -y= ln(-22 +.C) Step 6: y = - In(-22 +C) Is Daniela's work correct? If not, what is her mistake? Choose 1 answer: Step 1 is incorrect. The separation of variables wasn't...
[For questions 10-15] Consider the following multiple regression model with two right-hand-side variables. Y; = bo...
[For questions 10-15] Consider the following multiple regression model with two right-hand-side variables. Y; = bo + by Xli + b2 X 2 +e Question 10 1 pts Please answer whether the following equation is true or false. Y; = bo + b1 X1 + b2 X2i True False D Question 11 1 pts Please answer whether the following equation is true or false. et =Y - Ý True O False
Problem RMTE1.2 The left panel represents the graph of f(y), the right-hand-side of the differential equation/(). Sketc...
Problem RMTE1.2 The left panel represents the graph of f(y), the right-hand-side of the differential equation/(). Sketch the solutions on the right panel and determine the dt nature of the equilibrium points 0.4 2.0 0.2 1.6 y1 1.2 0.0 0.8 0.2 0.4 0.0 -0.4 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 (a)Y1 asymptotically stable; y2 unstable (c) yi-unstable; y2 semi-s (b) yi asymptotically stable; y2 semi-stable able (d) yi-unstable; y2 asymptotically stable...
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)
#4 Solve the following: (1 point) Solve the differential equation 6y 2 +2 where y 6...
#4 Solve the following: (1 point) Solve the differential equation 6y 2 +2 where y 6 when 0 (1 point) The differential equation can be written in differential form: M(x, y) dz +N(z, ) dy-0 where ,and N(x, y)--y5-3x The term M(, y) dz + N(x, y) dy becomes an exact differential if the left hand side above is divided by y4. Integrating that new equation, the solution of the differential equation is E C
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the...
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y =...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
Use the Laplace Transform method to solve the IVP y" - 8y + 16y = t4...
Use the Laplace Transform method to solve the IVP y" - 8y + 16y = t4 y(0) = 1,5(0) - 4. Show all your work Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y() which will...
please solve with steps and explain thanks Question 5 Given the differential equation y'' + 5y'...
please solve with steps and explain thanks
Question 5 Given the differential equation y'' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(8) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y...
Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y + 16y = 14 y(0) = 1,5/(0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y (s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the...
Daniela tried to solve the differential equation dy d: 9 = 22.e-y. This is her work: 9 = 22. e-y d Step 1: Je="dy= [ 23 dx Step 2: . ev = x² + a Step 3: e-*= -+C Step 4: In(e-y) = ln(-x? + C) Step 5: -y= ln(-22 +.C) Step 6: y = - In(-22 +C) Is Daniela's work correct? If not, what is her mistake? Choose 1 answer: Step 1 is incorrect. The separation of variables wasn't...
[For questions 10-15] Consider the following multiple regression model with two right-hand-side variables. Y; = bo + by Xli + b2 X 2 +e Question 10 1 pts Please answer whether the following equation is true or false. Y; = bo + b1 X1 + b2 X2i True False D Question 11 1 pts Please answer whether the following equation is true or false. et =Y - Ý True O False
Problem RMTE1.2 The left panel represents the graph of f(y), the right-hand-side of the differential equation/(). Sketch the solutions on the right panel and determine the dt nature of the equilibrium points 0.4 2.0 0.2 1.6 y1 1.2 0.0 0.8 0.2 0.4 0.0 -0.4 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 (a)Y1 asymptotically stable; y2 unstable (c) yi-unstable; y2 semi-s (b) yi asymptotically stable; y2 semi-stable able (d) yi-unstable; y2 asymptotically stable...
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)
#4 Solve the following: (1 point) Solve the differential equation 6y 2 +2 where y 6 when 0 (1 point) The differential equation can be written in differential form: M(x, y) dz +N(z, ) dy-0 where ,and N(x, y)--y5-3x The term M(, y) dz + N(x, y) dy becomes an exact differential if the left hand side above is divided by y4. Integrating that new equation, the solution of the differential equation is E C
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
Use the Laplace Transform method to solve the IVP y" - 8y + 16y = t4 y(0) = 1,5(0) - 4. Show all your work Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y() which will...
please solve with steps and explain thanks
Question 5 Given the differential equation y'' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(8) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y + 16y = 14 y(0) = 1,5/(0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y (s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the...
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