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

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\int \frac{y}{y ^{2} - 2 y - 3} d y

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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