14.11.17 problem 18 (b)

Internal problem ID [2610]
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 : 18 (b)
Date solved : Monday, January 27, 2025 at 06:04:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t^{{3}/{2}} {\mathrm e}^{3 t} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 19

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

\[ y = {\mathrm e}^{3 t} \left (c_2 +c_1 t +\frac {4 t^{{7}/{2}}}{35}\right ) \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 31

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

\[ y(t)\to \frac {1}{35} e^{3 t} \left (4 t^{7/2}+35 c_2 t+35 c_1\right ) \]