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

The solution for y^{''}+y=1,y(0)=0,y(1)=0 is y=-cos(t)+((cos(1)-1)sin(t))/(sin(1))+1

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

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

y = - cos (t) + \frac{( cos ( 1 ) - 1 ) sin ( t )}{sin ( 1 )} + 1

Solution steps

y^{''} (t) + y = 1

Solve linear ODE:

y = - cos (t) + \frac{( cos ( 1 ) - 1 ) sin ( t )}{sin ( 1 )} + 1

y = - cos (t) + \frac{( cos ( 1 ) - 1 ) sin ( t )}{sin ( 1 )} + 1

y^{^{''}} + 12 y^{^{'}} + 27 y = 64 e^{- 1 t}

y^{^{''}} + 4 y = 4 \cdot sec^{2} (2 t)

2 y^{^{''}} - 6 y^{^{'}} = 5, y (0) = 2, y^{^{'}} (0) = 1

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

y^{^{''}} + 5 y^{^{'}} + 6 y = 1, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}+y=1,y(0)=0,y(1)=0 ?
The solution for y^{''}+y=1,y(0)=0,y(1)=0 is y=-cos(t)+((cos(1)-1)sin(t))/(sin(1))+1