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 : Monday, January 27, 2025 at 09:23:45 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

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

dsolve([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)],singsol=all)
 

\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*}

✓ Solution by Mathematica

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

DSolve[{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)},{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*}