What is the solution for x^2-y^2+xy(dy)/(dx)=0 ?

The solution for x^2-y^2+xy(dy)/(dx)=0 is y=xsqrt(-2ln(x)+c_{1)},y=-xsqrt(-2ln(x)+c_{1)}

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x^2-y^2+xy(dy)/(dx)=0

x^{2} - y^{2} + x y \frac{d y}{d x} = 0

y = x - 2 ln (x) + c_{1}, y = - x - 2 ln (x) + c_{1}

Solution steps

x^{2} - y^{2} + x y \frac{d y}{d x} = 0

Solve Bernoulli ODE:

y = x - 2 ln (x) + c_{1}, y = - x - 2 ln (x) + c_{1}

y = x - 2 ln (x) + c_{1}, y = - x - 2 ln (x) + c_{1}

\int \frac{3 x}{( 6 - x ^{2} ) ^{3}} d x

\int \frac{( ln ( x ) ) ^{2} + 1}{x ln ( x )} d x

\frac{d ^{2}}{d t ^{2}} (cos^{2} (t))

\frac{d}{d x} (\frac{ln ( 3 x )}{x})

3 y^{^{''}} + 13 y^{^{'}} + 4 = 0, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for x^2-y^2+xy(dy)/(dx)=0 ?
The solution for x^2-y^2+xy(dy)/(dx)=0 is y=xsqrt(-2ln(x)+c_{1)},y=-xsqrt(-2ln(x)+c_{1)}