What is the solution for (dx)/(dt)-3x=cos(4t) ?

The solution for (dx)/(dt)-3x=cos(4t) is x=(4sin(4t))/(25)-(3cos(4t))/(25)+c_{1}e^{3t}

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(dx)/(dt)-3x=cos(4t)

\frac{d x}{d t} - 3 x = cos (4 t)

x = \frac{4 sin ( 4 t )}{25} - \frac{3 cos ( 4 t )}{25} + c_{1} e^{3 t}

Solution steps

\frac{d x}{d t} - 3 x = cos (4 t)

Solve linear ODE:

x = \frac{4 sin ( 4 t )}{25} - \frac{3 cos ( 4 t )}{25} + c_{1} e^{3 t}

x = \frac{4 sin ( 4 t )}{25} - \frac{3 cos ( 4 t )}{25} + c_{1} e^{3 t}

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

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

\frac{df}{d x} f (x) = cos (2 x)

(cos (7 x)) y^{^{'}} - 7 (tan (7 x)) y = 9 sec (7 x)

\int_{1}^{2} \frac{3}{x ^{4}} d x

What is the solution for (dx)/(dt)-3x=cos(4t) ?
The solution for (dx)/(dt)-3x=cos(4t) is x=(4sin(4t))/(25)-(3cos(4t))/(25)+c_{1}e^{3t}