Internal problem ID [5882]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.4 SPECIAL
FUNCTIONS. EXERCISES 6.4. Page 267
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+3 y^{\prime }+y x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(x*diff(y(x),x$2)+3*diff(y(x),x)+x^3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (\frac {x^{2}}{2}\right )}{x^{2}}+\frac {c_{2} \cos \left (\frac {x^{2}}{2}\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 43
DSolve[x*y''[x]+3*y'[x]+x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {i x^2}{2}} \left (2 c_1-i c_2 e^{i x^2}\right )}{2 x^2} \\ \end{align*}