Internal problem ID [12989]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page
90
Problem number: 4.4 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {x}{y}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)=x/y(x),y(x), singsol=all)
\begin{align*} y = \sqrt {x^{2}+c_{1}} y = -\sqrt {x^{2}+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 35
DSolve[y'[x]==x/y[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*}