84.16.1 problem 8.10

Internal problem ID [22181]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 8. Linear first-order differential equations. Supplementary problems
Problem number : 8.10
Date solved : Thursday, October 02, 2025 at 08:33:38 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-7 y&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x)-7*y(x) = exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{x}}{6}+{\mathrm e}^{7 x} c_1 \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 21

ode=D[y[x],x]-7*y[x]==Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^x}{6}+c_1 e^{7 x} \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \left (C_{1} e^{6 x} - \frac {1}{6}\right ) e^{x} \]