29.6.9 problem 155

Internal problem ID [4755]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 155
Date solved : Monday, January 27, 2025 at 09:36:30 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(x*diff(y(x),x) = a*x^2+b*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {a \,x^{2}}{b -2}+x^{b} c_{1} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 24

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

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