Internal problem ID [6098]
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: 34.
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 }-y^{\prime } \left (2 x -y^{\prime }\right )=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 5, y^{\prime }\left (-1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 20
dsolve([x^2*diff(y(x),x$2)=diff(y(x),x)*(2*x-diff(y(x),x)),y(-1) = 5, D(y)(-1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{2}-2 x +4 \ln \left (x +2\right )+\frac {5}{2} \]
✓ Solution by Mathematica
Time used: 0.878 (sec). Leaf size: 22
DSolve[{x^2*y''[x]==y'[x]*(2*x-y'[x]),{y[-1]==5,y'[-1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} ((x-4) x+8 \log (x+2)+5) \\ \end{align*}