1. find the solution of the initial-value problem:
dy/dx = (sin(3x))/(2+cos(3x)), y=4 when x=0
using equation: (f'(x))/(f(x)) dx = ln(f(x)) +c (f(x) > 0) when integrating.
2. a. find in implicit form, the general solution of the differential equation:
dy/dx = (4y^(1/2)(e^-x -e^x))/ ((e^x +e^-x)^2) (y>0)
b. find the corresponding explicit form of this general solution.
c. find the corresponding particular solution that satisfies the initial condition y=1 when x=0.
d. what is the value of y given by this particular solution when x=0.5 ? (give answer to 4 decimal places).
This solution is comprised of a detailed explanation to find the solution of the initial-value problem.