40.5.2 problem 18

Internal problem ID [6667]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page 65
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:18:40 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

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

\begin{align*} y &= \frac {x^{2}}{2}+c_1 \\ y &= \frac {x +c_1}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 32

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

\begin{align*} y(x)\to \frac {x^2}{2}+c_1 \\ y(x)\to \frac {x+c_1}{x} \\ y(x)\to 1 \\ \end{align*}