8.8.3 problem 23

Internal problem ID [840]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.2, second order linear equations. Page 311
Problem number : 23
Date solved : Monday, January 27, 2025 at 03:09:33 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=11 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 16

dsolve([diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=6,y(0) = 3, D(y)(0) = 11],y(x), singsol=all)
 

\[ y = 4 \,{\mathrm e}^{3 x}+{\mathrm e}^{-x}-2 \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 19

DSolve[{D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]==6,{y[0]==3,Derivative[1][y][0] ==11}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x}+4 e^{3 x}-2 \]