4.7.18 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 : Tuesday, September 30, 2025 at 04:31:54 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*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 15

ode:=2*diff(diff(y(x),x),x)-3*diff(y(x),x)+y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = 1/2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to 3 e^{x/2}-e^x \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 3*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): 1/2} 
dsolve(ode,func=y(x),ics=ics)
 

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