29.5.28 problem 145

Internal problem ID [4745]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 145
Date solved : Monday, January 27, 2025 at 09:36:14 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

\[ y \left (x \right ) = \frac {x^{4}+4 c_{1}}{4 x} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x^3}{4}+\frac {c_1}{x} \]