What is the solution for (dy)/(dt)=6y+cos(3t) ?

The solution for (dy)/(dt)=6y+cos(3t) is y=(sin(3t))/(15)-(2cos(3t))/(15)+c_{1}e^{6t}

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(dy)/(dt)=6y+cos(3t)

\frac{d y}{d t} = 6 y + cos (3 t)

y = \frac{sin ( 3 t )}{15} - \frac{2 cos ( 3 t )}{15} + c_{1} e^{6 t}

Solution steps

\frac{d y}{d t} = 6 y + cos (3 t)

Solve linear ODE:

y = \frac{sin ( 3 t )}{15} - \frac{2 cos ( 3 t )}{15} + c_{1} e^{6 t}

y = \frac{sin ( 3 t )}{15} - \frac{2 cos ( 3 t )}{15} + c_{1} e^{6 t}

\int (\frac{t ^{2} + t + 1}{( t + 3 ) ^{3}}) d t

- y + 10 e^{- t} = y^{^{'}}

\int ln (6 x) d x

sin (2 t) + cos (2 t)

\int sin^{3} (3 θ) cos (3 θ) d θ

What is the solution for (dy)/(dt)=6y+cos(3t) ?
The solution for (dy)/(dt)=6y+cos(3t) is y=(sin(3t))/(15)-(2cos(3t))/(15)+c_{1}e^{6t}