29.12.25 problem 344

Internal problem ID [4944]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 344
Date solved : Monday, January 27, 2025 at 09:53:16 AM
CAS classification : [_linear]

\begin{align*} x^{3} y^{\prime }&=3-x^{2}+x^{2} y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(x^3*diff(y(x),x) = 3-x^2+x^2*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 16

DSolve[x^3 D[y[x],x]==3 -x^2+x^2 y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{x^2}+c_1 x+1 \]