Internal problem ID [5324]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-x \left (-1+y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.041 (sec). Leaf size: 32
DSolve[x*(y'[x])^2+(y[x]-1-x^2)*y'[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*}