76.15.10 problem 10

Internal problem ID [17651]
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 : 10
Date solved : Tuesday, January 28, 2025 at 10:47:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve(4*diff(y(t),t$2)-4*diff(y(t),t)+y(t)=16*exp(t/2),y(t), singsol=all)
 

\[ y = {\mathrm e}^{\frac {t}{2}} \left (c_{1} t +2 t^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 25

DSolve[4*D[y[t],{t,2}]-4*D[y[t],t]+y[t]==16*Exp[t/2],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{t/2} \left (2 t^2+c_2 t+c_1\right ) \]