8.8.2 problem 22

Internal problem ID [839]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.2, second order linear equations. Page 311
Problem number : 22
Date solved : Monday, January 27, 2025 at 03:09:32 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y&=12 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

dsolve([diff(y(x),x$2)-4*y(x)=12,y(0) = 0, D(y)(0) = 10],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

DSolve[{D[y[x],{x,2}]-4*y[x]==12,{y[0]==0,Derivative[1][y][0] ==10}},y[x],x,IncludeSingularSolutions -> True]
 

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