45.3.20 problem 22(b)

Internal problem ID [7278]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G. Zill. 9th edition. Brooks/Cole. CA, USA.
Section : Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.3.1 page 250
Problem number : 22(b)
Date solved : Wednesday, March 05, 2025 at 04:22:32 AM
CAS classification : [[_Emden, _Fowler]]

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

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 28

Order:=6; 
ode:=x*diff(diff(y(x),x),x)+diff(y(x),x)-7*x^3*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \left (c_{2} \ln \left (x \right )+c_{1} \right ) \left (1+\frac {7}{16} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\left (-\frac {7}{32} x^{4}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 39

ode=x*D[y[x],{x,2}]+D[y[x],x]-7*x^3*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (\frac {7 x^4}{16}+1\right )+c_2 \left (\left (\frac {7 x^4}{16}+1\right ) \log (x)-\frac {7 x^4}{32}\right ) \]

✓ Sympy. Time used: 0.848 (sec). Leaf size: 15

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,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{1} \left (\frac {7 x^{4}}{16} + 1\right ) + O\left (x^{6}\right ) \]