Solve the following differential equations: cos^2(x - 2y) = 1 - 2 dy/dx

Question

Solve the following differential equations:

\(cos^2(x - 2y)= 1 - 2\frac{dy}{dx}\)

Answer 1

Given Differential equation is:

Differentiating w.r.t x on both sides we get,

Substitute (2) in (1) we get,

Bringing like variables on same side (i.e., variable seperable technique) we get,

Integrating on both sides we get,

⇒ ∫sec²zdz = ∫dx

We know that:

(1) ∫sec²xdx = tanx + C

(2) ∫adx = ax + C

⇒ tanz = x + C

Since z = x – 2y we substitute this,

⇒ tan(x – 2y) = x + C

∴ The solution for the given Differential Equation is tan(x – 2y) = x + C.