Internal problem ID [782]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=\frac {4 x_{1}\relax (t ) t^{3}-2 x_{2}\relax (t ) t^{3}+1}{t^{3}}\\ x_{2}^{\prime }\relax (t )&=\frac {8 x_{1}\relax (t ) t^{2}-4 x_{2}\relax (t ) t^{2}-1}{t^{2}} \end {align*}
✓ Solution by Maple
Time used: 0.027 (sec). Leaf size: 47
dsolve([diff(x__1(t),t)=4*x__1(t)-2*x__2(t)+1/(t^3),diff(x__2(t),t)=8*x__1(t)-4*x__2(t)-1/(t^2)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {c_{1} t}{2}-2 \ln \relax (t )+\frac {c_{1}}{8}+\frac {c_{2}}{2}+\frac {2}{t}-\frac {1}{2 t^{2}} \] \[ x_{2}\relax (t ) = \frac {5}{t}-4 \ln \relax (t )+c_{1} t +c_{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 61
DSolve[{x1'[t]==4*x1[t]-2*x2[t]+1/(t^3),x2'[t]==8*x1[t]-4*x2[t]-1/(t^2)},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to -\frac {1}{2 t^2}+\frac {2}{t}-2 \log (t)+4 c_1 t-2 c_2 t-2+c_1 \\ \text {x2}(t)\to \frac {5}{t}-4 \log (t)+8 c_1 t-4 c_2 t-4+c_2 \\ \end{align*}