75.33.2 problem 831

Internal problem ID [17284]
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 : 831
Date solved : Tuesday, January 28, 2025 at 09:58:53 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.642 (sec). Leaf size: 15

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

\[ x \left (t \right ) = -\left (t +1\right ) \left (t^{2}+t +1\right ) \]

✓ Solution by Mathematica

Time used: 0.185 (sec). Leaf size: 45

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

\[ x(t)\to e^{3 t} \left (\int _0^te^{-3 K[1]} \left (3 K[1]^3+3 K[1]^2+2 K[1]+1\right )dK[1]-1\right ) \]