78.8.48 problem 48

Internal problem ID [18246]
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 : 48
Date solved : Tuesday, January 28, 2025 at 11:44:10 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {x^{2}}{-x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.136 (sec). Leaf size: 23

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

\begin{align*} y(x)\to -\frac {x^2}{x-c_1} \\ y(x)\to 0 \\ \end{align*}