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

The solution for y^{''}+y=x,y(pi)=0,y(0)=0 is y=picos(x)+c_{2}sin(x)+x

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

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

y = π cos (x) + c_{2} sin (x) + x

Solution steps

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

Solve linear ODE:

y = π cos (x) + c_{2} sin (x) + x

y = π cos (x) + c_{2} sin (x) + x

y^{^{''}} - 12 y^{^{'}} + 36 y = 4 e^{6 x}

y^{^{''}} + 3 y^{^{'}} + 5 y = sin (t), y (0) = 1, y (0) = 0

x^{^{''}} - 25 x = 3 e^{2 t}

(D^{3} + 3 D^{2} - 4) y = x e^{- 2 x}

y^{^{''}} - y = 1, y (0) = 0

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