Internal problem ID [838]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 6.2, The Laplace Transform. Solution of Initial Value Problems. page
255
Problem number: 13.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1, y^{\prime \prime }\relax (0) = 0, y^{\prime \prime \prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 19
dsolve([diff(y(t),t$4)-4*diff(y(t),t$3)+6*diff(y(t),t$2)-4*diff(y(t),t)+y(t)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {t \,{\mathrm e}^{t} \left (2 t^{2}-3 t +3\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 22
DSolve[{y''''[t]-4*y'''[t]+6*y''[t]-4*y'[t]+y[t]==0,{y[0]==0,y'[0]==1,y''[0]==0,y'''[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^t t (t (2 t-3)+3) \\ \end{align*}