Question

solve the differential equations

dy/dx=cosx

Answer 1

 

Find dy/dx y=cos(x)

y=cos(x)y=cos(x)

Differentiate both sides of the equation.

ddx(y)=ddx(cos(x))ddx(y)=ddx(cos(x))

The derivative of yy with respect to xx is y'y′.

y'y′

The derivative of cos(x)cos(x) with respect to xx is −sin(x)-sin(x).

−sin(x)-sin(x)

Reform the equation by setting the left side equal to the right side.

y'=−sin(x)y′=-sin(x)

Replace y'y′ with dydxdydx.

dydx=−sin(x)