12.7.10 problem 10

Internal problem ID [1720]
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 : 10
Date solved : Monday, January 27, 2025 at 05:32:30 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y^{2}+\left (x y^{2}+6 y x +\frac {1}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 38

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

\[ \frac {x y^{6}+y^{3}-3 y^{2}-{\mathrm e}^{-y} c_1 +6 y-6}{y^{6}} = 0 \]

✓ Solution by Mathematica

Time used: 0.213 (sec). Leaf size: 41

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

\[ \text {Solve}\left [x=-\frac {y(x)^3-3 y(x)^2+6 y(x)-6}{y(x)^6}+\frac {c_1 e^{-y(x)}}{y(x)^6},y(x)\right ] \]