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

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

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

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

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

Solution steps

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

Solve using substitution:

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

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

\int sin^{3} (x) cos^{\frac{3}{2}} (x) d x

x \frac{d y}{d x} - 3 y = x y^{4}

x \to 0 lim ((1 - 3 x)^{\frac{2}{x}})

\int \frac{1}{( x ^{2} - 4 x + 5 ) ^{2}} d x

f (x) = 3 x^{2} + x - 2, at x = 1

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