Solve this differential equation

Ask iit jee aieee pet cbse icse state board community

Discussion Response Post to: Solve this differential equation

Forum Index -> Integral Calculus -> View Full Question

Author

Message

Yagyadutt Mishra (5432)

Forum Expert

total posts: 1984
Offline

cos(x+y) dy = dx
Let x+y = t
dt/dx = 1 + dy/dx
dy/dx = dt/dx - 1

Substitue in the main equation dy = dx . sec(x+y)
dy/dx = sec(x+y)
dt/dx - 1 = cos(t)
dt/dx = cost(t) + 1
dt/dx = 2.cos^2(t/2)

sec^2(t/2) dt = 2.dx
integrate both side !
2.tan(t/2) = 2x + 2C
tan(t/2) = x + C
t/2 = arctan(x+C)
t = 2.arctan(x+C)
y = 2.arctan(x+C) - x

Where C is the constant !