81.4.2 problem 2

Internal problem ID [18656]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 48
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 12:08:55 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)+2*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{x \left (\sqrt {3}-1\right )}+c_{2} {\mathrm e}^{-x \left (1+\sqrt {3}\right )} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 34

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

\[ y(x)\to e^{-\left (\left (1+\sqrt {3}\right ) x\right )} \left (c_2 e^{2 \sqrt {3} x}+c_1\right ) \]