39.1.6 problem Problem 11.6

Internal problem ID [6511]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.6
Date solved : Monday, January 27, 2025 at 02:10:49 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=50 t^{3}-36 t^{2}-63 t +18 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(t),t$2)-6*diff(y(t),t)+25*y(t)=50*t^3-36*t^2-63*t+18,y(t), singsol=all)
 

\[ y = {\mathrm e}^{3 t} \sin \left (4 t \right ) c_2 +{\mathrm e}^{3 t} \cos \left (4 t \right ) c_1 +2 t^{3}-3 t \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 38

DSolve[D[y[t],{t,2}]-6*D[y[t],t]+25*y[t]==50*t^3-36*t^2-63*t+18,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 t^3-3 t+c_2 e^{3 t} \cos (4 t)+c_1 e^{3 t} \sin (4 t) \]