Internal problem ID [3029]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 1(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } y=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)*y(x)=x,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {x^{2}+c_{1}} y \left (x \right ) = -\sqrt {x^{2}+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 35
DSolve[y'[x]*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x^2+2 c_1} y(x)\to \sqrt {x^2+2 c_1} \end{align*}