26.7.33 problem Exercise 20, problem 34, page 220

Internal problem ID [7083]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20, problem 34, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:14 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.091 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+20*y(x) = 0; 
ic:=[y(1/2*Pi) = 1, D(y)(1/2*Pi) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \left (-\frac {\sin \left (4 x \right )}{4}+\cos \left (4 x \right )\right ) {\mathrm e}^{-\pi +2 x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-4*D[y[x],x]+20*y[x]==0; 
ic={y[Pi/2]==1,Derivative[1][y][Pi/2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} e^{2 x-\pi } (4 \cos (4 x)-\sin (4 x)) \end{align*}

✓ Sympy. Time used: 0.117 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(20*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(pi/2): 1, Subs(Derivative(y(x), x), x, pi/2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (- \frac {\sin {\left (4 x \right )}}{4 e^{\pi }} + \frac {\cos {\left (4 x \right )}}{e^{\pi }}\right ) e^{2 x} \]