Quiz Solve the above equation to find its general solution.
Question: Solve the above equation to find its general solution.
The correct answer is –
To solve the above equation, we need to separate the variables v and x. Dividing both sides by (v2 – 1), we get:
dv/dx + (2v/y)/(v2 – 1) = 0
Multiplying both sides by (1/v), we get:
(1/v) dv/dx + (2/y) / (v2 – 1) = 0
Substituting u = 1/v, we get:
du/dx – (2/y)/(1 – u2) = 0
Separating the variables u and x, we get:
∫ (1 – u2) du = ∫ (2/y) dx
Solving the integrals, we get:
u = c1 cos(x/c2) v = 1/u = c2/(c1 cos(x/c2)) y = vx = c2x/(c1 cos(x/c2))
Therefore, the general solution of the given differential equation is y = (c2/c1) x sec(x/c2)