find the general solution to the differential equation.

Question

dy/dx=secxtanx-e^x

Answer 1

The equation is separable, meaning that we can put x and y on each side of the equal sign.

dy/dx=secxtanx-e^x
=>
dy = (sec(x)tan(x) - e^x)dx

Integrate both sides:

∫dy = ∫(sec(x)tan(x) - e^x)dx
=>
y = sec(x)-e^x + C
where C is an integration constant.

differentiate the above solution to confirm that the solution is correct.