76.13.54 problem 63

Internal problem ID [17565]
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 : 63
Date solved : Monday, March 31, 2025 at 04:17:40 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 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: 0.106 (sec). Leaf size: 23

ode:=4*x^2*diff(diff(y(x),x),x)+8*x*diff(y(x),x)+17*y(x) = 0; 
ic:=y(1) = 2, D(y)(1) = -3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {-\sin \left (2 \ln \left (x \right )\right )+2 \cos \left (2 \ln \left (x \right )\right )}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 26

ode=4*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]+17*y[x]==0; 
ic={y[1]==2,Derivative[1][y][1] ==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 \cos (2 \log (x))-\sin (2 \log (x))}{\sqrt {x}} \]

✓ Sympy. Time used: 0.216 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) + 8*x*Derivative(y(x), x) + 17*y(x),0) 
ics = {y(1): 2, Subs(Derivative(y(x), x), x, 1): -3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {- \sin {\left (2 \log {\left (x \right )} \right )} + 2 \cos {\left (2 \log {\left (x \right )} \right )}}{\sqrt {x}} \]