Internal problem ID [5689]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT
KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4}=9 t^{3}+64} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = {\frac {63}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.703 (sec). Leaf size: 26
dsolve([diff(y(t),t$2)+3*diff(y(t),t)+225/100*y(t)=9*t^3+64,y(0) = 1, D(y)(0) = 63/2],y(t), singsol=all)
\[ y \left (t \right ) = 4 t^{3}+{\mathrm e}^{-\frac {3 t}{2}} t -16 t^{2}+{\mathrm e}^{-\frac {3 t}{2}}+32 t \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 28
DSolve[{y''[t]+3*y'[t]+225/100*y[t]==9*t^3+64,{y[0]==1,y'[0]==315/10}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 4 t \left (t^2-4 t+8\right )+e^{-3 t/2} (t+1) \]