Internal problem ID [2998]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 250.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-a -b x -c \,x^{2}-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x) = a+b*x+c*x^2+x*y(x),y(x), singsol=all)
\[ y \relax (x ) = -b +x c \ln \relax (x )-\frac {a}{2 x}+c_{1} x \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 26
DSolve[x^2 y'[x]==a+b x+c x^2+x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a}{2 x}-b+c x \log (x)+c_1 x \\ \end{align*}