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

The solution for y^{''}+y=t(1+sin(t)) is y=c_{1}cos(t)+c_{2}sin(t)+t+(-t^2cos(t)+tsin(t))/4

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

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

y = c_{1} cos (t) + c_{2} sin (t) + t + \frac{- t ^{2} cos ( t ) + t sin ( t )}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + t + \frac{- t ^{2} cos ( t ) + t sin ( t )}{4}

y = c_{1} cos (t) + c_{2} sin (t) + t + \frac{- t ^{2} cos ( t ) + t sin ( t )}{4}

f (x) = x^{4} + x^{2} + 2

x \to 4 lim (\frac{a x ^{4}}{x - 4})

\int e^{5 x} x d x

f (x) = e^{- x + 1} - e^{- x + 1} x

\int \frac{1}{z} - \frac{x}{y ^{2}} d y

What is the solution for y^{''}+y=t(1+sin(t)) ?
The solution for y^{''}+y=t(1+sin(t)) is y=c_{1}cos(t)+c_{2}sin(t)+t+(-t^2cos(t)+tsin(t))/4