12.7.15 problem 15

Internal problem ID [1725]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 15
Date solved : Monday, January 27, 2025 at 05:33:16 AM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 20

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

\[ y x \left (x +y\right ) {\mathrm e}^{-y^{2}}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.172 (sec). Leaf size: 37

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

\[ \text {Solve}\left [x^2 \left (-e^{-y(x)^2}\right ) y(x)-x e^{-y(x)^2} y(x)^2=c_1,y(x)\right ] \]