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

The solution for (dy)/(dx)=(2y+sqrt(x^2-y^2))/(2x) is y=sin(1/2 ln(x)+c_{1})x

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

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

y = sin (\frac{1}{2} ln (x) + c_{1}) x

Solution steps

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

Solve using substitution:

y = sin (\frac{1}{2} ln (x) + c_{1}) x

y = sin (\frac{1}{2} ln (x) + c_{1}) x

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