What is the solution for x*y^'-y= 5/4*x*ln(x) ?

The solution for x*y^'-y= 5/4*x*ln(x) is y= 5/8 ln^2(x)x+c_{1}x

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xy^'-y= 5/4x*ln(x)

x \cdot y^{^{'}} - y = \frac{5}{4} \cdot x \cdot ln (x)

y = \frac{5}{8} ln^{2} (x) x + c_{1} x

Solution steps

x \cdot y^{'} (x) - y = \frac{5}{4} \cdot x \cdot ln (x)

Solve linear ODE:

y = \frac{5}{8} ln^{2} (x) x + c_{1} x

y = \frac{5}{8} ln^{2} (x) x + c_{1} x

\int \frac{x}{1 + 2 x ^{2}} d x

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

\int 50 + 3 x^{2} - \frac{3}{2} x d x

\int \frac{8 x ^{2}}{4 x ^{2} + 7} d x

\frac{d}{d x} (- \frac{4}{( 2 x + 1 ) ^{2}})

What is the solution for x*y^'-y= 5/4*x*ln(x) ?
The solution for x*y^'-y= 5/4*x*ln(x) is y= 5/8 ln^2(x)x+c_{1}x