82.7.7 problem 34-9

Internal problem ID [21863]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 34. Simulataneous linear differential equations. Page 1118
Problem number : 34-9
Date solved : Thursday, October 02, 2025 at 08:03:02 PM
CAS classification : system_of_ODEs

\begin{align*} 2 \frac {d}{d t}x \left (t \right )-3 \frac {d}{d t}y \left (t \right )&=2 \,{\mathrm e}^{2 t}\\ \frac {d}{d t}x \left (t \right )-2 \frac {d}{d t}y \left (t \right )&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.054 (sec). Leaf size: 19

ode:=[2*diff(x(t),t)-3*diff(y(t),t) = 2*exp(2*t), diff(x(t),t)-2*diff(y(t),t) = 0]; 
ic:=[x(0) = 0, y(0) = 1]; 
dsolve([ode,op(ic)]);
 

\begin{align*} x \left (t \right ) &= 2 \,{\mathrm e}^{2 t}-2 \\ y \left (t \right ) &= {\mathrm e}^{2 t} \\ \end{align*}

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 22

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

\begin{align*} x(t)&\to 2 \left (e^{2 t}-1\right )\\ y(t)&\to e^{2 t} \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 17

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

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