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}

x \to 2 - lim (\frac{4}{( x - 2 ) ^{3}})

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

\frac{d}{d x} ((sinh (x^{2}))^{\frac{1}{x}})

\frac{\partial}{\partial y} (5 x^{4} y)

\frac{d}{d x} (5^{x} - 1)

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}