47.2.47 problem 43

Internal problem ID [7463]
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 : 43
Date solved : Monday, January 27, 2025 at 03:01:07 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 45

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

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

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 49

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

\begin{align*} y(x)\to -\frac {\sqrt {x}}{\sqrt {-\log (x)+c_1}} \\ y(x)\to \frac {\sqrt {x}}{\sqrt {-\log (x)+c_1}} \\ y(x)\to 0 \\ \end{align*}