What is the solution for (dx)/(dt)-4x=cos(3t),x(0)=-1 ?

The solution for (dx)/(dt)-4x=cos(3t),x(0)=-1 is x=(3sin(3t))/(25)-(4cos(3t))/(25)-21/25 e^{4t}

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(dx)/(dt)-4x=cos(3t),x(0)=-1

\frac{d x}{d t} - 4 x = cos (3 t), x (0) = - 1

x = \frac{3 sin ( 3 t )}{25} - \frac{4 cos ( 3 t )}{25} - \frac{21}{25} e^{4 t}

Solution steps

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

Solve linear ODE:

x = \frac{3 sin ( 3 t )}{25} - \frac{4 cos ( 3 t )}{25} - \frac{21}{25} e^{4 t}

x = \frac{3 sin ( 3 t )}{25} - \frac{4 cos ( 3 t )}{25} - \frac{21}{25} e^{4 t}

x \to - 2 lim ((x^{2} + 5 x)^{2})

t \to π lim (- 8 sin (\frac{t}{2}))

\frac{\partial}{\partial y} (x^{a} y^{b})

\int_{0}^{π} sec^{2} (x) d x

What is the solution for (dx)/(dt)-4x=cos(3t),x(0)=-1 ?
The solution for (dx)/(dt)-4x=cos(3t),x(0)=-1 is x=(3sin(3t))/(25)-(4cos(3t))/(25)-21/25 e^{4t}