Internal problem ID [6673]
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]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=t^{3}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (t \right ) = \frac {\left (-13 t +2\right ) {\mathrm e}^{2 t}}{8}+\frac {t^{3}}{4}+\frac {3 t^{2}}{4}+\frac {9 t}{8}+\frac {3}{4} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 35
DSolve[{y''[t]-4*y'[t]+4*y[t]==t^3,{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} \left (2 t^3+6 t^2+9 t+e^{2 t} (2-13 t)+6\right ) \]