+0  
 
+1
312
1
avatar+15 

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
avatar
+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

15 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.