What is the solution for (dy)/(dt)-4y=10sin(2t) ?

The solution for (dy)/(dt)-4y=10sin(2t) is y=-cos(2t)-2sin(2t)+c_{1}e^{4t}

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(dy)/(dt)-4y=10sin(2t)

\frac{d y}{d t} - 4 y = 10 sin (2 t)

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

Solution steps

\frac{d y}{d t} - 4 y = 10 sin (2 t)

Solve linear ODE:

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

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

\int \frac{3}{x ^{2} - x} d x

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

t \to 0 lim (tan (2 t))

\int \frac{4}{( y + 1 ) ^{2}} d y

x \cdot y^{2} \cdot y^{'} (x) = y + 1, y (5 e^{2}) = 3

What is the solution for (dy)/(dt)-4y=10sin(2t) ?
The solution for (dy)/(dt)-4y=10sin(2t) is y=-cos(2t)-2sin(2t)+c_{1}e^{4t}