Verify that the function y = a cos x + b sin x is a solution of the di

1.	Verify that the function y = a cos x + b sin x is a solution of the differential equation cos(dy/dx) + y sin x = b. dx
Answer» The given function is y = a cos x + b sin x Differentiating both sides with respect to x, we have dy/dx = -a sin x + b cos x Putting values of dy/dx and y in the given differential equation, we have L.H.S. = cos x (- a sin x + b cos x) + {a cos x + b sin x) sin x = – a sin x cos x + b cos² x + a sin x cos x + b sin² x = b (cos² x + sin² x) = b × 1 = b = R.H.S Thus, y = a cos x + b sin x is a solution of differential equation cos x(dy/dx) + y sin x = b.

Verify that the function y = a cos x + b sin x is a solution of the differential equation cos(dy/dx) + y sin x = b. dx

Answer»

The given function is y = a cos x + b sin x

Differentiating both sides with respect to x, we have

dy/dx = -a sin x + b cos x

Putting values of dy/dx and y in the given differential equation, we have

L.H.S. = cos x (- a sin x + b cos x) + {a cos x + b sin x) sin x

= – a sin x cos x + b cos² x + a sin x cos x + b sin² x

= b (cos² x + sin² x)

= b × 1 = b = R.H.S

Thus, y = a cos x + b sin x is a solution of differential equation

cos x(dy/dx) + y sin x = b.