Question

solve the seperable equation:
dy/dx= (sec^2)y/1+x^2

im not sure how to reach the final answer

Answer 1

cos^2(y)dy=(1+x^2)dx
1/2+cos(2y)/4=x+x^3/3 +c

Answer 2

thank you!

Answer 3

it says the answer is 2y + sin(2y) = 4 arctan x +C

Answer 4

dy/dx= (sec^2)y/1+x^2
dy/sec^2)y= (1+x^2)dx
(cos y)^2 dy=(1+x^2)dx integrating both,sides
2y + sin(2y) = 4 arctan x +C

Answer 5

thank you very much!

Answer 6

yw

Answer 7

sorry I read question wrong
cos^2(y)dy=(1/1+x^2)dx
y/2+sin(2y)/4=aractan(x)+C
2y+sin(2y)=arctan(x)+C