Internal problem ID [3780]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 528.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x \left (x +y\right ) y^{\prime }-y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(x*(x+y(x))*diff(y(x),x) = x^2+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = x \,{\mathrm e}^{-\operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {c_{1}}{2}} {\mathrm e}^{-\frac {1}{2}}}{2 \sqrt {x}}\right )-\frac {c_{1}}{2}-\frac {1}{2}-\frac {\ln \left (x \right )}{2}}+x \]
✓ Solution by Mathematica
Time used: 7.26 (sec). Leaf size: 35
DSolve[x(x+y[x])y'[x]==x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+2 x W\left (\frac {e^{\frac {-1+c_1}{2}}}{2 \sqrt {x}}\right ) y(x)\to x \end{align*}