The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equationy" +p(t)y' + g{t}y = g(t).(38)provided one solution yı of the corresponding homogeneous equation is known. Let y = r(t)y) and showthat y satisfies equation 38 if v is a solution ofy1(O" + (2y, ) + plt)yO = g(0).(39)Equation 39 is a first-order linear differential equation for r'. By solving equation 39 for v, integrating theresult to find v, and then multiplying by y1(O. you can find the general solution of equation 38. This methodsimultaneously finds both the second homogeneous solution and a particular solution.Use the method above to solve the differential equationty" – (1+t)y' +y = 5t°e, t > 0, y1 (t) = 1+t.Use C1, C2, ... for the constants of integration.

The given differential equation is; ty" -(1+t)y'+y=5t2e2t

The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y" +p(t)y' + q(t)y = g(). (38) provided one solution y of the corresponding homogeneous equation is known. Let y= ()y() and show that y satisfies equation 38 if v is a solution of yı(" + (2y,) + p(t)y = g(0). (39) Equation 39 is a first-order linear differential equation for v. By solving equation 39 for v, integrating the result to find v, and then multiplying by y1(O. you can find the general solution of equation 38. This method simultaneously finds both the second homogeneous solution and a particular solution. Use the method above to solve the differential equation ty" – (1+t)y' +y = 5t2e24, t > 0, y (t) = 1+ t. Use C1, C2, ... for the constants of integration.

The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y" +p(t)y' + q(t)y = g(). (38) provided one solution y of the corresponding homogeneous equation is known. Let y= ()y() and show that y satisfies equation 38 if v is a solution of yı(" + (2y,) + p(t)y = g(0). (39) Equation 39 is a first-order linear differential equation for v. By solving equation 39 for v, integrating the result to find v, and then multiplying by y1(O. you can find the general solution of equation 38. This method simultaneously finds both the second homogeneous solution and a particular solution. Use the method above to solve the differential equation ty" – (1+t)y' +y = 5t2e24, t > 0, y (t) = 1+ t. Use C1, C2, ... for the constants of integration.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation
y" +p(t)y' + g{t}y = g(t).
(38)
provided one solution yı of the corresponding homogeneous equation is known. Let y = r(t)y) and show
that y satisfies equation 38 if v is a solution of
y1(O" + (2y, ) + plt)yO = g(0).
(39)
Equation 39 is a first-order linear differential equation for r'. By solving equation 39 for v, integrating the
result to find v, and then multiplying by y1(O. you can find the general solution of equation 38. This method
simultaneously finds both the second homogeneous solution and a particular solution.
Use the method above to solve the differential equation
ty" – (1+t)y' +y = 5t°e, t > 0, y1 (t) = 1+t.
Use C1, C2, ... for the constants of integration.

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