78.12.15 problem 1 (o)

Internal problem ID [18302]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 1 (o)
Date solved : Tuesday, January 28, 2025 at 11:45:42 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 24

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

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