Question

Use the method of separation of variables to solve the following DEs: (a) d[y]/d[x] = (3x^2)/y (b) d[y]/d[x] = cos(x)/sin(2y) (C) (c) d[y]/d[x] = ...

Answer 1

To solve the differential equation (b) using separation of variables, identify the given equation, rewrite it, integrate both sides, and solve the integrals to find the solution for y.

Step-by-step explanation:

Solution for (b)

1. Identify the given equation: dy/dx = cos(x)/sin(2y)
2. Rewrite the equation as sin(2y)dy = cos(x)dx
3. Integrate both sides to find the solution: ∫sin(2y)dy = ∫cos(x)dx
4. Solve the integrals and simplify the equation to get the solution for y.