29.21.8 problem 584

Internal problem ID [5178]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 584
Date solved : Monday, January 27, 2025 at 10:17:58 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.254 (sec). Leaf size: 44

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

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