26.7.32 problem Exercise 20, problem 33, page 220

Internal problem ID [7082]
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 33, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:14 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.070 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 25

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

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

✓ Sympy. Time used: 0.099 (sec). Leaf size: 19

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

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