14.11.8 problem 8

Internal problem ID [2601]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.5. Method of judicious guessing. Excercises page 164
Problem number : 8
Date solved : Monday, January 27, 2025 at 06:02:23 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=\left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 24

dsolve(diff(y(t),t$2)-6*diff(y(t),t)+9*y(t)=(3*t^7-5*t^4)*exp(3*t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{3 t} \left (c_2 +c_1 t +\frac {1}{24} t^{9}-\frac {1}{6} t^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 32

DSolve[D[y[t],{t,2}]-6*D[y[t],t]+9*y[t]==(3*t^7-5*t^4)*Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{24} e^{3 t} \left (t^9-4 t^6+24 c_2 t+24 c_1\right ) \]