29.5.29 problem 146

Internal problem ID [4746]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 146
Date solved : Monday, January 27, 2025 at 09:36:16 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=1+x^{3}+y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(x*diff(y(x),x) = 1+x^3+y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {1}{2} x^{3}-1+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 18

DSolve[x D[y[x],x]==1+x^3+y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3}{2}+c_1 x-1 \]