What is the solution for x(dy)/(dx)=y+(x^2+y^2)^{1/2} ?

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

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x(dy)/(dx)=y+(x^2+y^2)^{1/2}

x \frac{d y}{d x} = y + (x^{2} + y^{2})^{\frac{1}{2}}

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

Solution steps

x \frac{d y}{d x} = y + (x^{2} + y^{2})^{\frac{1}{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}

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

\int e^{x} x cos (x) d x

f (x) = 1 - 2 x

x \to 6 lim (x^{3} + 4 x)

\frac{d}{d x} (ln (x^{7} sin^{2} (x)))

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