Question

Solve the following differential equations:

(i) (ydx - xdy) cot(x/y) = ny² dx 

(ii) (dy/dx) - x√(25 - x²) = 0

(iii) x cos y dy = e^x(x log x + 1)dx

(iv) tan y(dy/dx) = cos(x + y) + cos(x - y)

(v) dy/dx = tan²(x + y)

Answer 1

(i) (ydx - xdy) cot(x/y) = ny² dx 

Dividing throughout by 'y²'

(ii) (dy/dx) - x√(25 - x²) = 0

(iii) x cos y dy = e^x(x log x + 1)dx

(iv) tan y(dy/dx) = cos(x + y) + cos(x - y)

(v) dy/dx = tan²(x + y)

Let u = x + y 

Differentiating with respect to ‘x’