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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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