82.12.24 problem Ex. 26

Internal problem ID [18789]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 26
Date solved : Tuesday, January 28, 2025 at 12:17:28 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

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

\begin{align*} y \left (x \right ) &= \sqrt {x^{2} a +c_{1}} \\ y \left (x \right ) &= -\sqrt {x^{2} a +c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 39

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

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