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

The solution for y^{''}+y=cos(t),y(0)=0,y^'(0)=0 is y=(tsin(t))/2

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

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

y = \frac{t sin ( t )}{2}

Solution steps

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

Solve linear ODE:

y = \frac{t sin ( t )}{2}

y = \frac{t sin ( t )}{2}

x \to - 3 + lim (ln (x + 3))

(4 x^{2} - y^{2}) d x - x y d y = 0

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

\frac{d}{d x} (13 x e^{- x})

\frac{\partial}{\partial v} (\frac{1}{4} (u - v))

What is the solution for y^{''}+y=cos(t),y(0)=0,y^'(0)=0 ?
The solution for y^{''}+y=cos(t),y(0)=0,y^'(0)=0 is y=(tsin(t))/2