What is the solution for y^{''}+y=x^2+1,y(0)=6,y(1)=0 ?

The solution for y^{''}+y=x^2+1,y(0)=6,y(1)=0 is y=7cos(x)-(7cos(1)sin(x))/(sin(1))+x^2-1

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y^{''}+y=x^2+1,y(0)=6,y(1)=0

y^{^{''}} + y = x^{2} + 1, y (0) = 6, y (1) = 0

y = 7 cos (x) - \frac{7 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

Solution steps

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

Solve linear ODE:

y = 7 cos (x) - \frac{7 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

y = 7 cos (x) - \frac{7 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

y^{^{''}} + y^{^{'}} + 64 y = cos (2 x)

d (x) = 4 x^{7} + 10 x^{6} + 5 x - 2 (2 x^{7} + 5 x^{6} + 10)

2 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 3 y = x^{2} + 2 x - 1

y^{^{''}} + y = cos (x) + 3 sin (2 x)

y^{^{''}} + 49 y = x^{2} cos (7 x) + x e^{- 7 x}

What is the solution for y^{''}+y=x^2+1,y(0)=6,y(1)=0 ?
The solution for y^{''}+y=x^2+1,y(0)=6,y(1)=0 is y=7cos(x)-(7cos(1)sin(x))/(sin(1))+x^2-1