Find the function y(x) satisfying dy/dx=4x^-8/9 and y(-1)=-2

Question

Find the function y(x) satisfying dy/dx=4x^-8/9 and y(-1)=-2

Answer 1

This is an initial value problem, so

dy/dx=4x^-8/9 and if we simplify , we would get dy/dx=36x^-8.If we integrate both sides to get the original functions,

y(x)=-36/7*x^-7+c.To get the value of c, we are going to use the initial vale which is y(-1)=-2

-2=36/7+c

c=-50/7. If we put c back into the solution, we get y(x)=-36/7*x^-7-50/7

Answer 2

y = 36x^1/9 + C

-2 = -36 + C

and y = 36x^1/9 + 34