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

The solution for y^{''}+y=x,y(0)=2,y^'(0)=0 is y=2cos(x)-sin(x)+x

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

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

y = 2 cos (x) - sin (x) + x

Solution steps

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

Solve linear ODE:

y = 2 cos (x) - sin (x) + x

y = 2 cos (x) - sin (x) + x

\int 3 x^{2} - 8 x d x

f (x) = 3 1 + x

\int 0.6 x + 2 d x

\int 3 x 1 - 2 x^{2} d x

19 x

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