76.17.11 problem 20

Internal problem ID [17697]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.7 (Variation of parameters). Problems at page 280
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 11:01:16 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: 0.007 (sec). Leaf size: 46

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

\[ y = c_{2} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{2 t}+\left (\int g \left (t \right ) {\mathrm e}^{-3 t}d t \right ) {\mathrm e}^{3 t}-\left (\int g \left (t \right ) {\mathrm e}^{-2 t}d t \right ) {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.044 (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]
 

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