Internal problem ID [9431]
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: 0.172 (sec). Leaf size: 19
dsolve({diff(x(t),t)=a*x(t),diff(y(t),t)=b},{x(t), y(t)}, singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{a t} \] \[ y \left (t \right ) = b t +c_{2} \]
✓ Solution by Mathematica
Time used: 0.025 (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*}