84.16.3 problem 8.12

Internal problem ID [22183]
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 : 8.12
Date solved : Thursday, October 02, 2025 at 08:33:40 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-7 y&=\sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

\[ y = -\frac {2 \cos \left (2 x \right )}{53}-\frac {7 \sin \left (2 x \right )}{53}+{\mathrm e}^{7 x} c_1 \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to -\frac {7}{53} \sin (2 x)-\frac {2}{53} \cos (2 x)+c_1 e^{7 x} \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} e^{7 x} - \frac {7 \sin {\left (2 x \right )}}{53} - \frac {2 \cos {\left (2 x \right )}}{53} \]