Internal problem ID [5341]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 10. Singular solutions, Extraneous loci. Supplemetary problems. Page
74
Problem number: 13.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x {y^{\prime }}^{2}-2 y y^{\prime }+2 y=-x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 36
dsolve(x*diff(y(x),x)^2-2*y(x)*diff(y(x),x)+x+2*y(x)=0,y(x), singsol=all)
\begin{align*} y = -\frac {\left (\frac {\left (x +c_{1} \right )^{2}}{c_{1}^{2}}+1\right ) x}{-\frac {2 \left (x +c_{1} \right )}{c_{1}}+2} y = c_{1} x \end{align*}
✓ Solution by Mathematica
Time used: 0.153 (sec). Leaf size: 78
DSolve[x*y'[x]^2-2*y[x]*y'[x]+x+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} e^{-c_1} x^2+x-e^{c_1} y(x)\to -e^{c_1} x^2+x-\frac {e^{-c_1}}{2} y(x)\to x-\sqrt {2} x y(x)\to \left (1+\sqrt {2}\right ) x \end{align*}