47.2.53 problem 49

Internal problem ID [7469]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 49
Date solved : Monday, January 27, 2025 at 03:01:26 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 y+\left (x^{2} y+1\right ) x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 16

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

\[ y = \frac {1}{\operatorname {LambertW}\left (\frac {c_{1}}{x^{2}}\right ) x^{2}} \]

✓ Solution by Mathematica

Time used: 60.326 (sec). Leaf size: 33

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

\[ y(x)\to \frac {1}{x^2 W\left (\frac {e^{\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )}}{x^2}\right )} \]