Hello,

What is the general solution of the following differential equation?

(1 + (x^3/y)sin^2x)dx + (1/y)(x + (1/cos^2(2y))dy = 0;
I used the integrating factor, but I'm stuck at the following step:
u(x) [-x^3sin^2x + 1] = u'(x) [x + (1/cos^2(2y)]

Thanks in advance!

Question

Hello,

What is the general solution of the following differential equation?

(1 + (x^3/y)sin^2x)dx + (1/y)(x + (1/cos^2(2y))dy = 0;
I used the integrating factor, but I'm stuck at the following step:
 u(x) [-x^3sin^2x + 1] = u'(x) [x + (1/cos^2(2y)]
 
Thanks in advance!

anonymous · Answer

The original eq is: $$(1 + (x ^{3}/y)\sin ^{2} x)dx + (1/y)(x + (1/\cos ^{2}(2y))dy = 0$$
I'm stuck at this step: $$u(x) [-xsin ^{2} x + 1] = u'(x) [x + (1/\cos ^{2}(2y)]$$