29.8.25 problem 230

Internal problem ID [4830]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 230
Date solved : Monday, January 27, 2025 at 09:41:47 AM
CAS classification : [_linear]

\begin{align*} \left (x +a \right ) y^{\prime }+b \,x^{2}+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

dsolve((a+x)*diff(y(x),x)+b*x^2+y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-b \,x^{3}+3 c_{1}}{3 x +3 a} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 25

DSolve[(a+x) D[y[x],x]+b x^2+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-b x^3+3 c_1}{3 (a+x)} \]