Internal problem ID [5487]
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]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.049 (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)
\[ y \relax (x ) = -\frac {x^{2}}{2}-c_{1} x -c_{1}^{2} \ln \left (-c_{1}+x \right )+c_{2} \]
✓ Solution by Mathematica
Time used: 0.479 (sec). Leaf size: 37
DSolve[x^2*y''[x]==2*x*y'[x]+(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} (x-c_1) (x+3 c_1)+c_1{}^2 (-\log (x-c_1))+c_2 \\ \end{align*}