29.22.5 problem 611

Internal problem ID [5205]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 611
Date solved : Monday, January 27, 2025 at 10:20:54 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 17

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

\[ \left (x^{2}+y \left (x \right )^{2}\right ) {\mathrm e}^{y \left (x \right )}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.162 (sec). Leaf size: 24

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

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