Internal problem ID [14920]
Internal file name [OUTPUT/14618_Tuesday_April_09_2024_02_06_08_AM_89691122/index.tex]
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.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "system of linear ODEs" Unable to solve or complete the solution.
Solve \begin {align*} x^{\prime }&=x^{2}\\ y^{\prime }\left (t \right )&={\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
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}{-t +c_{2}}\right \} \\ \{y \left (t \right ) &= {\mathrm e}^{t}+c_{1}\} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.107 (sec). Leaf size: 36
DSolve[{x'[t]==x[t]^2,y'[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*}