76.13.8 problem 8

Internal problem ID [17590]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 10:44:42 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(2*diff(y(x),x$2)-3*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {x}{2}}+{\mathrm e}^{x} c_{2} \]

✓ Solution by Mathematica

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

DSolve[2*D[y[x],{x,2}]-3*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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