12.6.10 problem 10

Internal problem ID [1689]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 10
Date solved : Monday, January 27, 2025 at 05:28:01 AM
CAS classification : [_rational]

\begin{align*} 2 x^{2}+8 y x +y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \end{align*}

✗ Solution by Maple

dsolve((2*x^2+8*x*y(x)+y(x)^2)+(2*x^2+x*y(x)^3/3)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(2*x^2+8*x*y[x]+y[x]^2)+(2*x^2+x*y[x]^3/3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved