A Find y in terms of x if dy dx x 8 y 5 and y06 yx B For wh

A. Find y in terms of x if

dy dx =x 8 y ?5

and y(0)=6.

y(x)= .

B. For what x -interval is the solution defined?
(Your answers should be numbers or plus or minus infinity. For plus infinity enter \"PINF\"; for minus infinity enter \"MINF\".)

The solution is defined on the interval:
<x<

Solution

dy/dx =x⁸ y^-5

and y(0)=6.

y⁵?dy=x⁸dx

integrating both sides

y⁶/6=x⁹/9+c

6⁶/6=0+c

c=6⁵=7776

y(x)=(2x⁹/3+6⁶)^1/6

solution defind for

MINF<x<PINF