Internal problem ID [6076]
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: 10.
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=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (2) = -1, y^{\prime }\relax (2) = -{\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 16
dsolve([x*diff(y(x),x$2)+diff(y(x),x)+x=0,y(2) = -1, D(y)(2) = -1/2],y(x), singsol=all)
\[ y \relax (x ) = -\frac {x^{2}}{4}+\ln \relax (x )-\ln \relax (2) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 19
DSolve[{x*y''[x]+y'[x]+x==0,{y[2]==-1,y'[2]==-1/2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (\frac {x}{2}\right )-\frac {x^2}{4} \\ \end{align*}