What is the solution for y^{''}+y=t,y(0)=0,y^'(0)=1 ?

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

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y^{''}+y=t,y(0)=0,y^'(0)=1

y^{^{''}} + y = t, y (0) = 0, y^{^{'}} (0) = 1

y = t

Solution steps

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

Solve linear ODE:

y = t

y = t

y^{^{''}} + 9 y = 8 sec (3 x)

y^{^{''}} + 16 y = 3 e^{8 x}

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

4 y^{^{''}} + 2 y = 4 x^{3} + 5 x^{2} - x + 7

y^{^{''}} - 3 y^{^{'}} + 2 y = cos (x), y^{^{'}} (0) = 2, y (0) = 0

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