10.10.11 problem 11

Internal problem ID [1343]
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
Date solved : Monday, January 27, 2025 at 04:51:49 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 46

dsolve(diff(y(t),t$2)-5*diff(y(t),t)+6*y(t) = g(t),y(t), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{3 t}+{\mathrm e}^{2 t} c_1 +\left (\int g \left (t \right ) {\mathrm e}^{-3 t}d t \right ) {\mathrm e}^{3 t}-\left (\int g \left (t \right ) {\mathrm e}^{-2 t}d t \right ) {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 59

DSolve[D[y[t],{t,2}]-5*D[y[t],t]+6*y[t] == g[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{2 t} \left (\int _1^t-e^{-2 K[1]} g(K[1])dK[1]+e^t \int _1^te^{-3 K[2]} g(K[2])dK[2]+c_2 e^t+c_1\right ) \]