Internal problem ID [6240]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page
38
Problem number: 1(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x -{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 26
dsolve(x^2*diff(y(x),x$2)=2*x*diff(y(x),x)+(diff(y(x),x))^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2}}{2}-c_{1} x -c_{1}^{2} \ln \left (x -c_{1} \right )+c_{2} \]
✓ Solution by Mathematica
Time used: 0.435 (sec). Leaf size: 41
DSolve[x^2*y''[x]==2*x*y'[x]+(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^2}{2}-c_1 x-c_1{}^2 \log (x-c_1)+\frac {3 c_1{}^2}{2}+c_2 \]