67.2.9 problem Problem 1(i)

Internal problem ID [13966]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(i)
Date solved : Tuesday, January 28, 2025 at 06:10:31 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 23

dsolve(y(x)*diff(y(x),x)=1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 38

DSolve[y[x]*D[y[x],x]==1,y[x],x,IncludeSingularSolutions -> True]
 

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