29.13.12 problem 366

Internal problem ID [4966]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 366
Date solved : Monday, January 27, 2025 at 09:59:56 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 48

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

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

✓ Solution by Mathematica

Time used: 0.217 (sec). Leaf size: 49

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

\begin{align*} y(x)\to -\frac {x^{3/2}}{\sqrt {-a x+c_1}} \\ y(x)\to \frac {x^{3/2}}{\sqrt {-a x+c_1}} \\ y(x)\to 0 \\ \end{align*}