Dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
(1/y + y) dy = cos(x) dx
Integrating:
ln(y) + y²/2 = sin(x) + c
ln(1) + 1/2 = sin(0) + c
c = 1/2
Thus,
ln(y) + y²/2 = sin(x) + 1/2
Answer: b
Explanation: cube root is equal to the power of 1/3
Multiply the exponents 24/3=8
5x+ 10+ 15y
= 5*x+ 5*2+ 5*(3y)
= 5*(x+2+3y)
The final answer is 5(x+2+3y)~