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

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

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

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

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

Solution steps

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

Solve using substitution:

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

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

\int - t d t

x \to 3 lim (x (\frac{2}{x} + 5))

\int_{\frac{1}{7}}^{5} 12 x ln (7 x) d x

y = e^{- 4 x}

x^{3} + 8, x + 8

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