Question

Help please i don’t know how to do it

Answer 1

Explanation:

`(dy)/(dx)=x^(2)(y-1)\\(1)/(y-1) \text{ } dy=x^(2) \text{ } dx\\\int (1)/(y-1) \text{ } dy=\int x^(2) \text{ } dx\\\ln|y-1|=(x^(3))/(3)+C\\`

From the initial condition,

`\ln|3-1|=(0^(3))/(3)+C\\\ln 2=C`

So we have that
`\ln |y-1|=(x^(3))/(3)+\ln 2\\e^{(x^(3))/(3)+\ln 2}=y-1\\2e^{(x^(3))/(3)}=y-1\\y=2e^{(x^(3))/(3)}+1`