60.9.1 problem 1856

Internal problem ID [11855]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1856
Date solved : Monday, January 27, 2025 at 11:43:50 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=a x \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=b \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 18

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: 0.022 (sec). Leaf size: 36

DSolve[{D[x[t],t]==a*x[t],D[y[t],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*}