Internal problem ID [6685]
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: 68.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=\operatorname {Heaviside}\left (t -1\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve([diff(y(t),t$2)-5*diff(y(t),t)+6*y(t)=Heaviside(t-1),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{3 t}-{\mathrm e}^{2 t}+\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{3 t -3}}{3}-\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{2 t -2}}{2}+\frac {\operatorname {Heaviside}\left (t -1\right )}{6} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 60
DSolve[{y''[t]-5*y'[t]+6*y[t]==UnitStep[t-1],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} e^{2 t} \left (-1+e^t\right ) & t\leq 1 \\ \frac {1}{6}-e^{2 t}+e^{3 t}-\frac {1}{2} e^{2 t-2}+\frac {1}{3} e^{3 t-3} & \text {True} \\ \end {array} \\ \end {array} \]