Question

If dy/dx = 5x^2y and y(0)=6, find an equation for y in terms of x

Answer 1

fun we have a function of y times a function of x=y' so we can use separation of variables

Answer 2

so we have dy=5x^2y dx => dy/y=5x^2 dx => integrate both sides: lny=5x^3/3+C

Answer 3

Now if you want to solve y just base e both sides giving you y=e^(5x^3/3+C)

Answer 4

Ok but we can find C since you are given the initial condition y(0)=6

Answer 5

y(0)=e^(0+C)=e^C=6 => so we have e^C=6 or C=ln6

Answer 6

y=e^(5x^3/3+ln6)

Answer 7

Now wasn't that fun? :)