Internal problem ID [2267]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 t^{2}-5 x \left (t \right )\\ y^{\prime }\left (t \right )&=-y \left (t \right )+{\mathrm e}^{3 t} \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 37
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: 0.216 (sec). Leaf size: 50
DSolve[{x'[t]+5*x[t]==3*t^2,y'[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*}