76.15.7 problem 7

Internal problem ID [17648]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 10:47:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=2 \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

dsolve(diff(y(t),t$2)-5*diff(y(t),t)+4*y(t)=2*exp(t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{4 t} c_{1} -\frac {2 \,{\mathrm e}^{t} \left (t -\frac {3 c_{2}}{2}\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 30

DSolve[D[y[t],{t,2}]-5*D[y[t],t]+4*y[t]==2*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{9} e^t \left (-6 t+9 c_2 e^{3 t}-2+9 c_1\right ) \]