Solve the first order linear D.E. (y +1)Cosxdx = dy where the G.S. is given y e^∫p(x)dx = ∫Q(x) e^∫p(x)dx + C

zzzzz Aug 4, 2017

#1**+1 **

Solve the separable equation ( dy(x))/( dx) = (y(x) + 1) cos(x):

Divide both sides by y(x) + 1:

(( dy(x))/( dx))/(y(x) + 1) = cos(x)

Integrate both sides with respect to x:

integral(( dy(x))/( dx))/(y(x) + 1) dx = integral cos(x) dx

Evaluate the integrals:

log(y(x) + 1) = sin(x) + c_1, where c_1 is an arbitrary constant.

Solve for y(x):

y(x) = e^(sin(x) + c_1) - 1

Simplify the arbitrary constants:

**Answer: | y(x) = c_1 e^(sin(x)) - 1**

Guest Aug 4, 2017