78.8.33 problem 33

Internal problem ID [18231]
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 : 33
Date solved : Tuesday, January 28, 2025 at 11:42:51 AM
CAS classification : [_linear]

\begin{align*} \frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve((y(x)-x)/(x+y(x))^3 -  2*x/(x+y(x))^3  * diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -x +\sqrt {x}\, c_{1} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 17

DSolve[(y[x]-x)/(x+y[x])^3 -  2*x/(x+y[x])^3  * D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x+c_1 \sqrt {x} \]