Internal problem ID [10179]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1856.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=a x \left (t \right )\\ y^{\prime }\left (t \right )&=b \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve({diff(x(t),t)=a*x(t),diff(y(t),t)=b},singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{a t} \\ y \left (t \right ) &= b t +c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 36
DSolve[{x'[t]==a*x[t],y'[t]==b},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{a t} \\ y(t)\to b t+c_2 \\ x(t)\to 0 \\ y(t)\to b t+c_2 \\ \end{align*}