Internal problem ID [3526]
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]
\[ \boxed {x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) = \frac {x}{\sqrt {c_{1} {\mathrm e}^{2 x}-1}} y \left (x \right ) = -\frac {x}{\sqrt {c_{1} {\mathrm e}^{2 x}-1}} \end{align*}
✓ Solution by Mathematica
Time used: 4.843 (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*}