Internal problem ID [3758]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 506.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {x y y^{\prime }-y^{2}=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x*y(x)*diff(y(x),x) = x+y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {x \left (c_{1} x -2\right )} \\ y \left (x \right ) &= -\sqrt {x \left (c_{1} x -2\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.31 (sec). Leaf size: 42
DSolve[x y[x] y'[x]==x+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {-2+c_1 x} \\ y(x)\to \sqrt {x} \sqrt {-2+c_1 x} \\ \end{align*}