40.9.2 problem 12

Internal problem ID [6712]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 12
Date solved : Wednesday, March 05, 2025 at 02:39:55 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=5 \end{align*}

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

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x) = 5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{4 x} c_1}{4}-\frac {5 x}{4}+c_2 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-4*D[y[x],x]==5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {5 x}{4}+\frac {1}{4} c_1 e^{4 x}+c_2 \]

✓ Sympy. Time used: 0.189 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{4 x} - \frac {5 x}{4} \]