66.1.38 problem Problem 52

Internal problem ID [13885]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 52
Date solved : Tuesday, January 28, 2025 at 06:07:23 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

\[ y = \frac {7 x^{3}}{x^{7}+7 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.183 (sec). Leaf size: 25

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

\begin{align*} y(x)\to \frac {7 x^3}{x^7+7 c_1} \\ y(x)\to 0 \\ \end{align*}