74.22.4 problem 4

Internal problem ID [16651]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 08:25:52 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=x^{2}\\ y^{\prime }\left (t \right )&={\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 20

dsolve([diff(x(t),t)=x(t)^2,diff(y(t),t)=exp(t)],singsol=all)
 

\begin{align*} \left \{x \left (t \right ) &= \frac {1}{c_{2} -t}\right \} \\ \{y &= {\mathrm e}^{t}+c_{1}\} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 36

DSolve[{D[x[t],t]==x[t]^2,D[y[t],t]==Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -\frac {1}{t+c_1} \\ y(t)\to e^t+c_2 \\ x(t)\to 0 \\ y(t)\to e^t+c_2 \\ \end{align*}