34.2.2 problem 2

Internal problem ID [6032]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter 2, Equations of the first order and degree. page 20
Problem number : 2
Date solved : Monday, January 27, 2025 at 01:33:57 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

\[ y = -\frac {2}{a \,x^{2}-2 c_1} \]

✓ Solution by Mathematica

Time used: 0.135 (sec). Leaf size: 24

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

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