78.6.10 problem 2 (j)

Internal problem ID [18178]
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. Section 10 (Linear equations). Problems at page 82
Problem number : 2 (j)
Date solved : Tuesday, January 28, 2025 at 11:36:20 AM
CAS classification : [_linear]

\begin{align*} y-2 y x -x^{2}+x^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

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

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

\[ y = x^{2} \left (1+{\mathrm e}^{\frac {1}{x}} c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 19

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

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