Internal problem ID [5920]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page
297
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+4 y-t^{3}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 30
dsolve([diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=t^3,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (-13 t +2\right ) {\mathrm e}^{2 t}}{8}+\frac {t^{3}}{4}+\frac {3 t^{2}}{4}+\frac {9 t}{8}+\frac {3}{4} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 32
DSolve[{y''[t]-4*y'[t]+4*y[t]==t^3,{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{8} \left (e^{2 t} (2-13 t)+t (2 t (t+3)+9)+6\right ) \\ \end{align*}