Internal problem ID [6075]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime }-x^{5}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = {\frac {1}{2}}, y^{\prime }\relax (1) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([x*diff(y(x),x$2)=diff(y(x),x)+x^5,y(1) = 1/2, D(y)(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{24} x^{6}+\frac {3}{8} x^{2}+\frac {1}{12} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 19
DSolve[{x*y''[x]==y'[x]+x^5,{y[1]==1/2,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} \left (x^6+9 x^2+2\right ) \\ \end{align*}