Internal problem ID [2041]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.4, page 36
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y-y^{\prime } x -3+2 y^{\prime } x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(y(x)-x*diff(y(x),x)=3-2*x^2*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-\frac {3}{x}+c_{1}\right ) x}{2 x -1} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 24
DSolve[y[x]-x*y'[x]==3-2*x^2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3+c_1 x}{1-2 x} \\ y(x)\to 3 \\ \end{align*}