29.21.5 problem 581

Internal problem ID [5175]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 581
Date solved : Monday, January 27, 2025 at 10:17:42 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 42

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

\begin{align*} y \left (x \right ) &= \frac {\sqrt {x^{{10}/{3}} \left (-2 x^{{1}/{3}}+c_{1} \right )}}{x^{{7}/{3}}} \\ y \left (x \right ) &= -\frac {\sqrt {x^{{10}/{3}} \left (-2 x^{{1}/{3}}+c_{1} \right )}}{x^{{7}/{3}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.723 (sec). Leaf size: 47

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

\begin{align*} y(x)\to -\sqrt {-\frac {2}{x}+\frac {c_1}{x^{4/3}}} \\ y(x)\to \sqrt {-\frac {2}{x}+\frac {c_1}{x^{4/3}}} \\ \end{align*}