Internal problem ID [10205]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1882.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right )&={\mathrm e}^{2 t}\\ 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )&=0 \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 118
dsolve([2*diff(x(t),t)+diff(y(t),t)-3*x(t)=0,diff(x(t),t$2)+diff(y(t),t)-2*y(t)=exp(2*t)],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {{\mathrm e}^{2 t}}{4}+c_{1} {\mathrm e}^{t}-\frac {7 c_{2} {\mathrm e}^{\frac {t}{2}} \cos \left (\frac {\sqrt {23}\, t}{2}\right )}{18}-\frac {c_{2} {\mathrm e}^{\frac {t}{2}} \sqrt {23}\, \sin \left (\frac {\sqrt {23}\, t}{2}\right )}{18}-\frac {7 c_{3} {\mathrm e}^{\frac {t}{2}} \sin \left (\frac {\sqrt {23}\, t}{2}\right )}{18}+\frac {c_{3} {\mathrm e}^{\frac {t}{2}} \sqrt {23}\, \cos \left (\frac {\sqrt {23}\, t}{2}\right )}{18} \\ y \left (t \right ) &= -\frac {{\mathrm e}^{2 t}}{8}+c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{\frac {t}{2}} \cos \left (\frac {\sqrt {23}\, t}{2}\right )+c_{3} {\mathrm e}^{\frac {t}{2}} \sin \left (\frac {\sqrt {23}\, t}{2}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.668 (sec). Leaf size: 199
DSolve[{2*x'[t]+y'[t]-3*x[t]==0,x''[t]+y'[t]-2*y[t]==Exp[2*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{276} e^{t/2} \left (23 e^{t/2} \left (3 e^t+6 c_1+2 c_2+4 c_3\right )+46 (3 c_1-c_2-2 c_3) \cos \left (\frac {\sqrt {23} t}{2}\right )-2 \sqrt {23} (9 c_1-11 c_2+2 c_3) \sin \left (\frac {\sqrt {23} t}{2}\right )\right ) \\ y(t)\to -\frac {1}{552} e^{t/2} \left (23 e^{t/2} \left (3 e^t-4 (3 c_1+c_2+2 c_3)\right )+92 (3 c_1+c_2-4 c_3) \cos \left (\frac {\sqrt {23} t}{2}\right )-4 \sqrt {23} (33 c_1-25 c_2-8 c_3) \sin \left (\frac {\sqrt {23} t}{2}\right )\right ) \\ \end{align*}