What is the solution for x^2y^'+2xy=7cos^2(x) ?

The solution for x^2y^'+2xy=7cos^2(x) is y=(7(2x+sin(2x)))/(4x^2)+(c_{1})/(x^2)

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x^2y^'+2xy=7cos^2(x)

x^{2} y^{^{'}} + 2 x y = 7 cos^{2} (x)

y = \frac{7 ( 2 x + sin ( 2 x ) )}{4 x ^{2}} + \frac{c _{1}}{x ^{2}}

Solution steps

x^{2} y^{'} (x) + 2 x y = 7 cos^{2} (x)

Solve linear ODE:

y = \frac{7 ( 2 x + sin ( 2 x ) )}{4 x ^{2}} + \frac{c _{1}}{x ^{2}}

y = \frac{7 ( 2 x + sin ( 2 x ) )}{4 x ^{2}} + \frac{c _{1}}{x ^{2}}

\int (\frac{sin ( 2 x )}{cos ( x )}) d x

\frac{d}{d x} (\frac{x ^{6}}{5})

\frac{d}{d x} (\frac{y}{x + y})

f (x) = - \frac{1}{7} (x^{- 7} - x^{14})

x csc (x)

What is the solution for x^2y^'+2xy=7cos^2(x) ?
The solution for x^2y^'+2xy=7cos^2(x) is y=(7(2x+sin(2x)))/(4x^2)+(c_{1})/(x^2)