72.9.15 problem 34

Internal problem ID [14811]
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
Date solved : Tuesday, January 28, 2025 at 07:17:04 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=1\\ y^{\prime }&=x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 20

dsolve([diff(x(t),t)=1,diff(y(t),t)=x(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 26

DSolve[{D[x[t],t]==1,D[y[t],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*}