Q. 65.0( 1 Vote )

# Solve the following differential equations:

Given Differential equation is:

We know that 1–cos2x = sin2x

……(1)

Let us assume z = x– 2y

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

……(2)

Substitute (2) in (1) we get,

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

We know that

sec2zdz = dx

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.

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