Internal problem ID [6069]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES
Page 324
Problem number: 2.
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 }+\left (y^{\prime }\right )^{2}-2 x y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 5, y^{\prime }\relax (2) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 24
dsolve([x^2*diff(y(x),x$2)+diff(y(x),x)^2-2*x*diff(y(x),x)=0,y(2) = 5, D(y)(2) = -4],y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{2}+3 x +9 \ln \left (x -3\right )-3-9 i \pi \]
✓ Solution by Mathematica
Time used: 0.887 (sec). Leaf size: 26
DSolve[{x^2*y''[x]+(y'[x])^2-2*x*y'[x]==0,{y[2]==5,y'[2]==-4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x (x+6)+9 \log (x-3)-9 i \pi -3 \\ \end{align*}