89.11.23 problem 23

Internal problem ID [24548]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 23
Date solved : Thursday, October 02, 2025 at 10:46:02 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=-4 \\ \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 17

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

\[ y = -2 \sqrt {2}\, {\mathrm e}^{x} \sin \left (\sqrt {2}\, x \right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to -2 \sqrt {2} e^x \sin \left (\sqrt {2} x\right ) \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 22

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

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