What is the solution for (dy)/(dx)+1/x y=3cos(2x) ?

The solution for (dy)/(dx)+1/x y=3cos(2x) is y=(3(2xsin(2x)+cos(2x))}{4x}+\frac{c_{1})/x

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(dy)/(dx)+1/x y=3cos(2x)

\frac{d y}{d x} + \frac{1}{x} y = 3 cos (2 x)

y = \frac{3 ( 2 x sin ( 2 x ) + cos ( 2 x ) )}{4 x} + \frac{c _{1}}{x}

Solution steps

\frac{d y}{d x} + \frac{1}{x} y = 3 cos (2 x)

Solve linear ODE:

y = \frac{3 ( 2 x sin ( 2 x ) + cos ( 2 x ) )}{4 x} + \frac{c _{1}}{x}

y = \frac{3 ( 2 x sin ( 2 x ) + cos ( 2 x ) )}{4 x} + \frac{c _{1}}{x}

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\frac{\partial}{\partial x} (x^{2} + y^{2} - 2)

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What is the solution for (dy)/(dx)+1/x y=3cos(2x) ?
The solution for (dy)/(dx)+1/x y=3cos(2x) is y=(3(2xsin(2x)+cos(2x))}{4x}+\frac{c_{1})/x