Internal problem ID [5885]
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: 22 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+y^{\prime }-7 y x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(x*diff(y(x),x$2)+diff(y(x),x)-7*x^3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \BesselI \left (0, \frac {\sqrt {7}\, x^{2}}{2}\right )+c_{2} \BesselK \left (0, \frac {\sqrt {7}\, x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 36
DSolve[x*y''[x]+y'[x]-7*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \, _0\tilde {F}_1\left (;1;\frac {7 x^4}{16}\right )+2 c_2 K_0\left (\frac {\sqrt {7} x^2}{2}\right ) \\ \end{align*}