40.1.4 problem 16

Internal problem ID [6572]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 2. Solutions of differential equations. Supplemetary problems. Page 11
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:12:33 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 43

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

\begin{align*} y &= \frac {\sqrt {\left (-x +c_1 \right ) x}\, x}{-x +c_1} \\ y &= \frac {\sqrt {\left (-x +c_1 \right ) x}\, x}{x -c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 47

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

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