29.9.11 problem 251

Internal problem ID [4851]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 251
Date solved : Monday, January 27, 2025 at 09:42:43 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }&=a +b x +c \,x^{2}-y x \end{align*}

✓ 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)
 

\[ y \left (x \right ) = \frac {c x}{2}+b +\frac {\ln \left (x \right ) a}{x}+\frac {c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 26

DSolve[x^2 D[y[x],x]==a+b x+c x^2-x y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {a \log (x)}{x}+b+\frac {c x}{2}+\frac {c_1}{x} \]