8.7.21 problem 37

Internal problem ID [827]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 37
Date solved : Monday, January 27, 2025 at 03:09:24 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

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

\[ y = c_1 \,{\mathrm e}^{-\frac {x}{2}}+c_2 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 22

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

\[ y(x)\to c_1 e^{-x/2}+c_2 e^x \]