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 : Wednesday, March 05, 2025 at 05:34:37 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

ode:=x*diff(diff(y(x),x),x)+diff(y(x),x)-7*x^3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.193 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-7*x**3*y(x) + x*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} I_{0}\left (\frac {\sqrt {7} x^{2}}{2}\right ) + C_{2} Y_{0}\left (\frac {\sqrt {7} i x^{2}}{2}\right ) \]