14.11.13 problem 13

Internal problem ID [2606]
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 : 13
Date solved : Monday, January 27, 2025 at 06:04:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 25

DSolve[D[y[t],{t,2}]-3*D[y[t],t]+2*y[t]==Exp[t]+Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (-t+e^t (t-1+c_2)-1+c_1\right ) \]