28.4.47 problem 7.47

Internal problem ID [4579]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 7. Systems of linear differential equations. Problems at page 351
Problem number : 7.47
Date solved : Tuesday, March 04, 2025 at 06:52:45 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+35 \,{\mathrm e}^{t} t^{{3}/{2}} \end{align*}

✓ Maple. Time used: 0.109 (sec). Leaf size: 47

ode:=[diff(x__1(t),t) = 3*x__1(t)-2*x__2(t), diff(x__2(t),t) = 2*x__1(t)-x__2(t)+35*exp(t)*t^(3/2)]; 
dsolve(ode);
 

\begin{align*} x_{1} \left (t \right ) &= -{\mathrm e}^{t} \left (8 t^{{7}/{2}}-c_{1} t -c_{2} \right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{t} \left (16 t^{{7}/{2}}-28 t^{{5}/{2}}-2 c_{1} t +c_{1} -2 c_{2} \right )}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 63

ode={D[x1[t],t]==3*x1[t]-2*x2[t],D[x2[t],t]==2*x1[t]-x2[t]+35*Exp[t]*t^(3/2)}; 
ic={}; 
DSolve[{ode,ic},{x1[t],x2[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {x1}(t)\to e^t \left (-8 t^{7/2}+2 (c_1-c_2) t+c_1\right ) \\ \text {x2}(t)\to e^t \left (-8 t^{7/2}+14 t^{5/2}+2 (c_1-c_2) t+c_2\right ) \\ \end{align*}

✓ Sympy. Time used: 0.221 (sec). Leaf size: 66

from sympy import * 
t = symbols("t") 
x__1 = Function("x__1") 
x__2 = Function("x__2") 
ode=[Eq(-3*x__1(t) + 2*x__2(t) + Derivative(x__1(t), t),0),Eq(-35*t**(3/2)*exp(t) - 2*x__1(t) + x__2(t) + Derivative(x__2(t), t),0)] 
ics = {} 
dsolve(ode,func=[x__1(t),x__2(t)],ics=ics)
 

\[ \left [ x^{1}{\left (t \right )} = 2 C_{1} t e^{t} - 8 t^{\frac {7}{2}} e^{t} + \left (C_{1} + 2 C_{2}\right ) e^{t}, \ x^{2}{\left (t \right )} = 2 C_{1} t e^{t} + 2 C_{2} e^{t} - 8 t^{\frac {7}{2}} e^{t} + 14 t^{\frac {5}{2}} e^{t}\right ] \]