What is the solution for (dy)/(dt)-5y=sin(2t) ?

The solution for (dy)/(dt)-5y=sin(2t) is y=-(2cos(2t))/(29)-(5sin(2t))/(29)+c_{1}e^{5t}

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(dy)/(dt)-5y=sin(2t)

\frac{d y}{d t} - 5 y = sin (2 t)

y = - \frac{2 cos ( 2 t )}{29} - \frac{5 sin ( 2 t )}{29} + c_{1} e^{5 t}

Solution steps

\frac{d y}{d t} - 5 y = sin (2 t)

Solve linear ODE:

y = - \frac{2 cos ( 2 t )}{29} - \frac{5 sin ( 2 t )}{29} + c_{1} e^{5 t}

y = - \frac{2 cos ( 2 t )}{29} - \frac{5 sin ( 2 t )}{29} + c_{1} e^{5 t}

y = 47 (2 t^{3} - 9)^{\frac{6}{5}}

\int \frac{3}{5 y - 4} d y

x \to 0 lim (\frac{6 x n - 5 x n - 1 - 7 x n - 2}{- 6 x n - 4 x n - 2})

f (x) = (x^{4} + 3 x^{2} - 2)^{5}

ln (s + 1)

What is the solution for (dy)/(dt)-5y=sin(2t) ?
The solution for (dy)/(dt)-5y=sin(2t) is y=-(2cos(2t))/(29)-(5sin(2t))/(29)+c_{1}e^{5t}