75.33.4 problem 833

Internal problem ID [17286]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 3. Section 24.2. Solving the Cauchy problem for linear differential equation with constant coefficients. Exercises page 249
Problem number : 833
Date solved : Tuesday, January 28, 2025 at 09:58:54 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} 2 x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=-{\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 9.600 (sec). Leaf size: 15

dsolve([2*diff(x(t),t)+6*x(t)=t*exp(-3*t),x(0) = -1/2],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {{\mathrm e}^{-3 t} \left (t^{2}-2\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 19

DSolve[{2*D[x[t],t]+6*x[t]==t*Exp[-3*t],{x[0]==-1/2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{4} e^{-3 t} \left (t^2-2\right ) \]