78.2.2 problem 1.b

Internal problem ID [20954]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 1.b
Date solved : Thursday, October 02, 2025 at 07:00:38 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.107 (sec). Leaf size: 20

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

\[ y = \frac {2 \sqrt {7}\, {\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {7}\, x}{2}\right )}{7} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to \frac {2 e^{3 x/2} \sin \left (\frac {\sqrt {7} x}{2}\right )}{\sqrt {7}} \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \frac {2 \sqrt {7} e^{\frac {3 x}{2}} \sin {\left (\frac {\sqrt {7} x}{2} \right )}}{7} \]