y Find the solution to the differential equation dtdyy24t y7

y=

Find the solution to the differential equation dtdy=y2(4+t) y=7whent=1. y=

Solution

dy/y^2=(4+t)dt -1/y=4t+t^2/2+c t=1 y=7 -1/7 =4+1/2+c c=-65/14 -1/y=4t+t^2/2-65/14 -1/y=(56t+7t^2-65)/14 y=-14/(56t+7t^2-65)