Internal problem ID [13075]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.1. page 258
Problem number: 34.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=1\\ y^{\prime }&=x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([diff(x(t),t)=1,diff(y(t),t)=x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} +t \\ y \left (t \right ) &= c_{2} t +\frac {1}{2} t^{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 26
DSolve[{x'[t]==1,y'[t]==x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to t+c_1 \\ y(t)\to \frac {t^2}{2}+c_1 t+c_2 \\ \end{align*}