78.8.39 problem 39

Internal problem ID [18237]
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 : 39
Date solved : Tuesday, January 28, 2025 at 11:43:17 AM
CAS classification : [_linear]

\begin{align*} {\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

dsolve(exp(x^2*y(x))*(1+2*x^2*y(x))+ x^3*exp(x^2*y(x)) * diff(y(x),x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 16

DSolve[Exp[x^2*y[x]]*(1+2*x^2*y[x])+ x^3*Exp[x^2*y[x]] * D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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