What is the solution for y^{''}-2y^'+2y=2x-2,y(pi)=pi,y(0)=0 ?

The solution for y^{''}-2y^'+2y=2x-2,y(pi)=pi,y(0)=0 is y=c_{2}e^xsin(x)+x

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y^{''}-2y^'+2y=2x-2,y(pi)=pi,y(0)=0

y^{^{''}} - 2 y^{^{'}} + 2 y = 2 x - 2, y (π) = π, y (0) = 0

y = c_{2} e^{x} sin (x) + x

Solution steps

y^{''} (x) - 2 y^{'} (x) + 2 y = 2 x - 2

Solve linear ODE:

y = c_{2} e^{x} sin (x) + x

y = c_{2} e^{x} sin (x) + x

What is the solution for y^{''}-2y^'+2y=2x-2,y(pi)=pi,y(0)=0 ?
The solution for y^{''}-2y^'+2y=2x-2,y(pi)=pi,y(0)=0 is y=c_{2}e^xsin(x)+x