76.13.55 problem 64

Internal problem ID [17566]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 64
Date solved : Monday, March 31, 2025 at 04:17:42 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=2\\ y^{\prime }\left (-1\right )&=3 \end{align*}

✓ Maple. Time used: 0.057 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+9*y(x) = 0; 
ic:=y(-1) = 2, D(y)(-1) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -9 x^{3} \left (i \pi -\ln \left (x \right )+\frac {2}{9}\right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 20

ode=x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+9*y[x]==0; 
ic={y[-1]==2,Derivative[1][y][-1] ==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^3 (9 \log (x)-9 i \pi -2) \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 9*y(x),0) 
ics = {y(-1): 2, Subs(Derivative(y(x), x), x, -1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{3} \left (9 \log {\left (x \right )} - 2 - 9 i \pi \right ) \]