What is the solution for xy^'=y+sqrt(x^2+y^2) ?

The solution for xy^'=y+sqrt(x^2+y^2) is y=-1/(2e^{c_{1)}}+(e^{c_{1}}x^2)/2

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xy^'=y+sqrt(x^2+y^2)

x y^{^{'}} = y + x^{2} + y^{2}

y = - \frac{1}{2 e ^{c_{1}}} + \frac{e ^{c_{1}} x ^{2}}{2}

Solution steps

x y^{'} (x) = y + x^{2} + y^{2}

Solve using substitution:

y = - \frac{1}{2 e ^{c_{1}}} + \frac{e ^{c_{1}} x ^{2}}{2}

y = - \frac{1}{2 e ^{c_{1}}} + \frac{e ^{c_{1}} x ^{2}}{2}

\int - 5 x^{3} d x

x \to 0 lim (\frac{sin ( k t )}{t})

5 x^{3}

x \to - 1 lim (ln (x^{2} - 1))

\frac{2 ^{k}}{3 k} x^{k}

What is the solution for xy^'=y+sqrt(x^2+y^2) ?
The solution for xy^'=y+sqrt(x^2+y^2) is y=-1/(2e^{c_{1)}}+(e^{c_{1}}x^2)/2