10.10.4 problem 4

Internal problem ID [1336]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page 190
Problem number : 4
Date solved : Monday, January 27, 2025 at 04:51:20 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: 0.019 (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]
 

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