75.6.15 problem 148

Internal problem ID [16700]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 148
Date solved : Monday, March 31, 2025 at 03:06:17 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y \ln \left (2\right )&=2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 14

ode:=diff(y(x),x)-y(x)*ln(2) = 2^sin(x)*(-1+cos(x))*ln(2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2^{x} c_1 +2^{\sin \left (x \right )} \]

✓ Mathematica. Time used: 0.364 (sec). Leaf size: 37

ode=D[y[x],x]-y[x]*Log[2]==2^(Sin[x])*(Cos[x]-1)*Log[2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 2^x \left (\int _1^x2^{\sin (K[1])-K[1]} (\cos (K[1])-1) \log (2)dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.543 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2**sin(x)*(cos(x) - 1)*log(2) - y(x)*log(2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2^{\sin {\left (x \right )}} + C_{1} e^{x \log {\left (2 \right )}} \]