54.1.9 problem 9

Internal problem ID [11323]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 07:40:24 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = c_1 \,{\mathrm e}^{x \left (\sin \left (\ln \left (x \right )\right )+a \right )} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 32

ode=D[y[x],x] - (Sin[Log[x]] + Cos[Log[x]] +a)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \exp \left (\int _1^x(a+\cos (\log (K[1]))+\sin (\log (K[1])))dK[1]\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.357 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} e^{x \left (a + \sin {\left (\log {\left (x \right )} \right )}\right )} \]