35.8.27 problem 27

Internal problem ID [6234]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 27
Date solved : Monday, January 27, 2025 at 01:49:39 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 12

dsolve([diff(y(x),x$2)+diff(y(x),x)-6*y(x)=6,y(0) = 1, D(y)(0) = 4],y(x), singsol=all)
 

\[ y = -1+2 \,{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 14

DSolve[{D[y[x],{x,2}]+D[y[x],x]-6*y[x]==6,{y[0]==1,Derivative[1][y][0] ==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^{2 x}-1 \]