What is the solution for (dx)/(dt)+7x=5cos(2t) ?

The solution for (dx)/(dt)+7x=5cos(2t) is x=(5(2sin(2t)+7cos(2t)))/(53)+(c_{1})/(e^{7t)}

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(dx)/(dt)+7x=5cos(2t)

\frac{d x}{d t} + 7 x = 5 cos (2 t)

x = \frac{5 ( 2 sin ( 2 t ) + 7 cos ( 2 t ) )}{53} + \frac{c _{1}}{e ^{7 t}}

Solution steps

\frac{d x}{d t} + 7 x = 5 cos (2 t)

Solve linear ODE:

x = \frac{5 ( 2 sin ( 2 t ) + 7 cos ( 2 t ) )}{53} + \frac{c _{1}}{e ^{7 t}}

x = \frac{5 ( 2 sin ( 2 t ) + 7 cos ( 2 t ) )}{53} + \frac{c _{1}}{e ^{7 t}}

n = 1 \sum \infty \frac{n ^{3}}{4 ^{n}}

x \to 1 lim ([g (x) - 3 f (x)])

\int e^{y} d y

\frac{\partial}{\partial y} (e^{y} + x)

f (x) = \frac{5}{x}

What is the solution for (dx)/(dt)+7x=5cos(2t) ?
The solution for (dx)/(dt)+7x=5cos(2t) is x=(5(2sin(2t)+7cos(2t)))/(53)+(c_{1})/(e^{7t)}