Internal problem ID [15568]
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: 845.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {2 x^{\prime \prime }-2 x^{\prime }=\left (1+t \right ) {\mathrm e}^{t}} \] With initial conditions \begin {align*} \left [x \left (0\right ) = {\frac {1}{2}}, x^{\prime }\left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 13
dsolve([2*diff(x(t),t$2)-2*diff(x(t),t)=(1+t)*exp(t),x(0) = 1/2, D(x)(0) = 1/2],x(t), singsol=all)
\[ x = \frac {{\mathrm e}^{t} \left (t^{2}+2\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 17
DSolve[{2*x''[t]-2*x'[t]==(1+t)*Exp[t],{x[0]==1/2,x'[0]==1/2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{4} e^t \left (t^2+2\right ) \]