What is the solution for (dy)/(dt)-4y=10sin(2t),y(0)=0 ?

The solution for (dy)/(dt)-4y=10sin(2t),y(0)=0 is y=-cos(2t)-2sin(2t)+e^{4t}

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(dy)/(dt)-4y=10sin(2t),y(0)=0

\frac{d y}{d t} - 4 y = 10 sin (2 t), y (0) = 0

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

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

\frac{d}{d x} (e^{arccsc (x)})

\frac{d}{d x} (- a sin (x) + b cos (x))

f (x) = 4 x

\frac{\partial}{\partial x} (- 15 (3 x + y)^{4})

y^{^{'}} = (y - 1)^{2}

What is the solution for (dy)/(dt)-4y=10sin(2t),y(0)=0 ?
The solution for (dy)/(dt)-4y=10sin(2t),y(0)=0 is y=-cos(2t)-2sin(2t)+e^{4t}