1.2 problem 3

Internal problem ID [14935]

Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 1. Basic concepts and definitions. Exercises page 18
Problem number: 3.
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 \left (x \right ) &= \sqrt {x^{2}+c_{1}} \\ y \left (x \right ) &= -\sqrt {x^{2}+c_{1}} \\ \end{align*}

Solution by Mathematica

Time used: 0.106 (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*}