52.3.20 problem 22 (b)

Internal problem ID [8306]
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)
Date solved : Monday, January 27, 2025 at 03:48:27 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x y^{\prime \prime }+y^{\prime }-7 x^{3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = c_{1} \operatorname {BesselI}\left (0, \frac {\sqrt {7}\, x^{2}}{2}\right )+c_{2} \operatorname {BesselK}\left (0, \frac {\sqrt {7}\, x^{2}}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 41

DSolve[x*D[y[x],{x,2}]+D[y[x],x]-7*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {BesselI}\left (0,\frac {\sqrt {7} x^2}{2}\right )+2 c_2 K_0\left (\frac {\sqrt {7} x^2}{2}\right ) \]