54.1.3 problem 3

Internal problem ID [11317]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 07:40:12 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+a y-b \sin \left (c x \right )&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 38

ode:=diff(y(x),x)+a*y(x)-b*sin(c*x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 35

ode=D[y[x],x] + a*y[x] - b*Sin[c*x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-a x} \left (\int _1^xb e^{a K[1]} \sin (c K[1])dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 39

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

\[ y{\left (x \right )} = C_{1} e^{- a x} + \frac {a b \sin {\left (c x \right )}}{a^{2} + c^{2}} - \frac {b c \cos {\left (c x \right )}}{a^{2} + c^{2}} \]