54.2.13 problem 15

Internal problem ID [8545]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number : 15
Date solved : Monday, January 27, 2025 at 04:13:32 PM
CAS classification : [_quadrature]

\begin{align*} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve(x*diff(y(x),x)^2-(x^2+1)*diff(y(x),x)+x=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 24

DSolve[x*(D[y[x],x])^2-(x^2+1)*D[y[x],x]+x==0,y[x],x,IncludeSingularSolutions -> True]
 

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