What is the solution for y^'=((5x^2+y^2))/(xy) ?

The solution for y^'=((5x^2+y^2))/(xy) is y=xsqrt(10ln(x)+c_{1)},y=-xsqrt(10ln(x)+c_{1)}

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y^'=((5x^2+y^2))/(xy)

y^{^{'}} = \frac{( 5 x ^{2} + y ^{2} )}{x y}

y = x 10 ln (x) + c_{1}, y = - x 10 ln (x) + c_{1}

Solution steps

y^{'} (x) = \frac{( 5 x ^{2} + y ^{2} )}{x y}

Solve Bernoulli ODE:

y = x 10 ln (x) + c_{1}, y = - x 10 ln (x) + c_{1}

y = x 10 ln (x) + c_{1}, y = - x 10 ln (x) + c_{1}

\int_{0}^{\frac{1}{2} - x} 384 x y d y

\int x (4 x^{2} + 7)^{9} d x

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

f^{^{''}} (x) = \frac{3}{4} x^{4} + 2 x^{3} - 12 x^{2} + 29

What is the solution for y^'=((5x^2+y^2))/(xy) ?
The solution for y^'=((5x^2+y^2))/(xy) is y=xsqrt(10ln(x)+c_{1)},y=-xsqrt(10ln(x)+c_{1)}