What is the solution for y^{''}+y=x^2+1,y(0)=7,y(1)=0 ?

The solution for y^{''}+y=x^2+1,y(0)=7,y(1)=0 is y=8cos(x)-(8cos(1)sin(x))/(sin(1))+x^2-1

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y^{''}+y=x^2+1,y(0)=7,y(1)=0

y^{^{''}} + y = x^{2} + 1, y (0) = 7, y (1) = 0

y = 8 cos (x) - \frac{8 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

Solution steps

y^{''} (x) + y = x^{2} + 1

Solve linear ODE:

y = 8 cos (x) - \frac{8 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

y = 8 cos (x) - \frac{8 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

8 y^{^{''}} + 2 y^{^{'}} - y = 9

y^{^{''}} - 8 y^{^{'}} + 15 y = 64 e^{t}

d (x) = (3 x - 1) (x - 2)^{- 1}

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

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 3 cos (x)

What is the solution for y^{''}+y=x^2+1,y(0)=7,y(1)=0 ?
The solution for y^{''}+y=x^2+1,y(0)=7,y(1)=0 is y=8cos(x)-(8cos(1)sin(x))/(sin(1))+x^2-1