90.19.1 problem 1

Internal problem ID [25283]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 4. Linear Constant Coefficient Differential Equations. Exercises at page 309
Problem number : 1
Date solved : Thursday, October 02, 2025 at 11:59:34 PM
CAS classification : system_of_ODEs

\begin{align*} y_{1}^{\prime }\left (t \right )-6 y_{1} \left (t \right )&=-4 y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=2 y_{1} \left (t \right ) \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right )&=2 \\ y_{2} \left (0\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 33

ode:=[diff(y__1(t),t)-6*y__1(t) = -4*y__2(t), diff(y__2(t),t) = 2*y__1(t)]; 
ic:=[y__1(0) = 2, y__2(0) = -1]; 
dsolve([ode,op(ic)]);
 

\begin{align*} y_{1} \left (t \right ) &= 6 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{2 t} \\ y_{2} \left (t \right ) &= 3 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{2 t} \\ \end{align*}

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 38

ode={D[y1[t],t]-6*y1[t]==-4*y2[t], D[y2[t],t]==2*y1[t]}; 
ic={y1[0]==2,y2[0]==-1}; 
DSolve[{ode,ic},{y1[t],y2[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {y1}(t)&\to 6 e^{4 t}-4 e^{2 t}\\ \text {y2}(t)&\to e^{2 t} \left (3 e^{2 t}-4\right ) \end{align*}

✓ Sympy. Time used: 0.068 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y1 = Function("y1") 
y2 = Function("y2") 
ode=[Eq(-6*y1(t) + 4*y2(t) + Derivative(y1(t), t),0),Eq(-2*y1(t) + Derivative(y2(t), t),0)] 
ics = {y1(0): 2, y2(0): -1} 
dsolve(ode,func=[y1(t),y2(t)],ics=ics)
 

\[ \left [ y_{1}{\left (t \right )} = 6 e^{4 t} - 4 e^{2 t}, \ y_{2}{\left (t \right )} = 3 e^{4 t} - 4 e^{2 t}\right ] \]