75.1.2 problem 3

Internal problem ID [16665]
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
Date solved : Tuesday, January 28, 2025 at 09:16:36 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (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: 0.079 (sec). Leaf size: 35

DSolve[D[y[x],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*}