Internal problem ID [693]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }+6 y-g \relax (t )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
dsolve(diff(y(t),t$2)-5*diff(y(t),t)+6*y(t) = g(t),y(t), singsol=all)
\[ y \relax (t ) = c_{2} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{2 t}+\left (\int g \relax (t ) {\mathrm e}^{-3 t}d t \right ) {\mathrm e}^{3 t}-\left (\int g \relax (t ) {\mathrm e}^{-2 t}d t \right ) {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 56
DSolve[y''[t]-5*y'[t]+6*y[t] == g[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{2 t} \left (\int _1^t-e^{-2 K[1]} g(K[1])dK[1]+e^t \left (\int _1^te^{-3 K[2]} g(K[2])dK[2]+c_2\right )+c_1\right ) \\ \end{align*}