73.1.5 problem 2.2 (e)

Internal problem ID [14983]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (e)
Date solved : Tuesday, January 28, 2025 at 07:26:32 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } y&=2 x \end{align*}

✓ Solution by Maple

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

dsolve(y(x)*diff(y(x),x)=2*x,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {2 x^{2}+c_{1}} \\ y &= -\sqrt {2 x^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 42

DSolve[y[x]*D[y[x],x]==2*x,y[x],x,IncludeSingularSolutions -> True]
 

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