please helppppppppp!

1. if dy/dx=(x^3 + 1)/(y) when x=1, then, when x=2, y=

a) radical 27/2 b) radical 27/8 c)+-radical 27/8 d)+-3/2 e)=+-radical 27/2

2. population p grows according to the equation dp/dt=kp, where k is a constant and t is measured in years. if the population doubles every 12 years then the calue of k is approcimately

a)3.583 b)1.792 c)0.693 d)0.279 e)0058

i dont kno this one
consider the differential equation dy/dx= (e^x - 1)/2y. if y=4, when x=0 what is the value of y when x=1

a. radical e+ 14
b. radical e+15
c. radical e^2 +11
d. radical e^2+15
e. radical e^2=12

please show me the step cause i dont kno these..thank u

There are three things that are useful to remember with differential equations:

1. Seperate- (eg. y dy= (x^3+1) dx for #1)

2. Integrate both sides

3. And dont forget the constant, C

Then you plug in the values of x and y to find C and then you can find the other x or y value.