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]]
\[ \boxed {4 y^{\prime \prime }-4 y^{\prime }+y-16 \,{\mathrm e}^{\frac {t}{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{\frac {t}{2}}+t \,{\mathrm e}^{\frac {t}{2}} c_{1} +2 t^{2} {\mathrm e}^{\frac {t}{2}} \]
✓ 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*}