72.12.13 problem 21(b)

Internal problem ID [14860]
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 3.5 page 327
Problem number : 21(b)
Date solved : Tuesday, January 28, 2025 at 07:17:47 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=-2 y\\ y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 14

dsolve([diff(x(t),t)=-2*y(t),diff(y(t),t)=0],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 18

DSolve[{D[x[t],t]==-2*y[t],D[y[t],t]==0*x[t]+0*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1-2 c_2 t \\ y(t)\to c_2 \\ \end{align*}