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

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

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(dy)/(dx)=(5x^2+y^2)/(xy)

\frac{d y}{d x} = \frac{5 x ^{2} + y ^{2}}{x y}

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

Solution steps

\frac{d y}{d 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}

\frac{d y}{d t} + \frac{1}{t} y = \frac{6}{t}, y (1) = 6

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

f (x) = 2 x - 6

\frac{d}{d t} (e^{t} + e^{- t})

f (x) = \frac{1}{11 x}

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