Internal problem ID [15556]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {2 x^{\prime }+6 x=t \,{\mathrm e}^{-3 t}} \] With initial conditions \begin {align*} \left [x \left (0\right ) = -{\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.391 (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: 0.063 (sec). Leaf size: 19
DSolve[{2*x'[t]+6*x[t]==t*Exp[-3*t],{x[0]==-1/2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{4} e^{-3 t} \left (t^2-2\right ) \]