10.7.18 problem 20

Internal problem ID [1266]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 20
Date solved : Monday, January 27, 2025 at 04:48:25 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 15

dsolve([2*diff(y(x),x$2) -3*diff(y(x),x)+y(x) = 0,y(0) = 2, D(y)(0) = 1/2],y(x), singsol=all)
 

\[ y = -{\mathrm e}^{x}+3 \,{\mathrm e}^{\frac {x}{2}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

DSolve[{2*D[y[x],{x,2}]-3*D[y[x],x]+y[x]==0,{y[0]==2,Derivative[1][y][0] ==1/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 e^{x/2}-e^x \]