10.4 problem 4

Internal problem ID [686]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {4 y^{\prime \prime }-4 y^{\prime }+y-16 \,{\mathrm e}^{\frac {t}{2}}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 27

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

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

Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 24

DSolve[4*y''[t]-4*y'[t]+y[t]== 16*Exp[t/2],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to e^{t/2} (t (2 t+c_2)+c_1) \\ \end{align*}