73.17.27 problem 27

Internal problem ID [15490]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 27
Date solved : Monday, March 31, 2025 at 01:39:20 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=2*diff(diff(y(x),x),x)-7*diff(y(x),x)+3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 \,{\mathrm e}^{\frac {7 x}{2}} c_1}{7}+\frac {3 x}{7}+c_2 \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 26

ode=2*D[y[x],{x,2}]-7*D[y[x],x]+3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {3 x}{7}+\frac {2}{7} c_1 e^{7 x/2}+c_2 \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-7*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{\frac {7 x}{2}} + \frac {3 x}{7} \]