78.8.12 problem 12

Internal problem ID [18210]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 11:39:03 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 11

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

\[ y(x)\to x (x+c_1) \]