Question

the solution of differential equation (dy\dx) + sin x =0

Answer 1

GIVEN :–

A differential equation (dy/dx) + sin(x) = 0.

TO FIND :–

Solution of differential equation .

SOLUTION :–

=> dy/dx + sin(x) = 0

=> dy/dx = - sin(x)

=> dy = - sin(x) dx

• Now integrate both side with respect to 'x' –

=> ∫dy = - ∫ sin(x).dx

=> y = - [-cos(x)] + c

=> y = cos(x) + c

Important formula :–

(1) ∫sin(x).dx = -cos(x) + c

(2) ∫cos(x).dx = sin(x) + c

(3) ∫ tan(x).dx = - ln(|cos(x)|) + c

(4) ∫cot(x).dx = ln(|sin(x)|) + c

(5) ∫sec²(x) = tan(x) + c