15.17.2 problem 2

Internal problem ID [3238]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 26, page 115
Problem number : 2
Date solved : Monday, January 27, 2025 at 07:27:17 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+5 x \left (t \right )&=3 t^{2}\\ \frac {d}{d t}y \left (t \right )+y \left (t \right )&={\mathrm e}^{3 t} \end{align*}

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 36

dsolve([diff(x(t),t)+5*x(t)=3*t^2,diff(y(t),t)+y(t)=exp(3*t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= \frac {3 t^{2}}{5}-\frac {6 t}{25}+\frac {6}{125}+c_2 \,{\mathrm e}^{-5 t} \\ y \left (t \right ) &= \frac {{\mathrm e}^{3 t}}{4}+{\mathrm e}^{-t} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 50

DSolve[{D[x[t],t]+5*x[t]==3*t^2,D[y[t],t]+y[t]==Exp[3*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {3 t^2}{5}-\frac {6 t}{25}+c_1 e^{-5 t}+\frac {6}{125} \\ y(t)\to \frac {e^{3 t}}{4}+c_2 e^{-t} \\ \end{align*}