Question

calculus help....
Which of the following families of functions is the solution to the differential equation? y' = 10xy

Answer 1

y = Cx^1/10......y=x^10+C......Ce^(5x^2)

Answer 2

i believe you can do separation of parameters so
dy/dx =10xy
dy/y=10xdx

dy/y = ln y
10xdx = 5x^2

raise each side to e to get y = e^(5x^2) and then the constant

Answer 3

because the 10xdx actually would be 5x^2 +c and raised to e is:
e^(5x^2+c) = e^(5x^2)*e^(c) which e^c is just a number so you can turn that into c or whatever letter you want for a constant

Answer 4

oh and separation of variable sorry, not parameters.

Answer 5

that's right htanks!