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

The solution for (dy)/(dt)=2y+sin(2t) is y=-(cos(2t))/4-(sin(2t))/4+c_{1}e^{2t}

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(dy)/(dt)=2y+sin(2t)

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d y}{d x} = \frac{2 x sec ( \frac{y}{x} ) + y}{x}

\frac{d}{d x} (6 3 x^{2} + 1)

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

x \to 0 lim (\frac{x ∣ x ∣}{x})

\int \frac{1}{x ^{2} + 7 x - 6} d x

What is the solution for (dy)/(dt)=2y+sin(2t) ?
The solution for (dy)/(dt)=2y+sin(2t) is y=-(cos(2t))/4-(sin(2t))/4+c_{1}e^{2t}