Internal problem ID [3018]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 270.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+\left (x^{2}+y^{2}-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(x^2*diff(y(x),x)+(x^2+y(x)^2-x)*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x}{\sqrt {-1+c_{1} {\mathrm e}^{2 x}}} \\ y \relax (x ) = -\frac {x}{\sqrt {-1+c_{1} {\mathrm e}^{2 x}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.592 (sec). Leaf size: 47
DSolve[x^2 y'[x]+(x^2+y[x]^2-x)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\sqrt {-1+c_1 e^{2 x}}} \\ y(x)\to \frac {x}{\sqrt {-1+c_1 e^{2 x}}} \\ y(x)\to 0 \\ \end{align*}