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Help please i don’t know how to do it

Help please i don’t know how to do it-example-1
User Hitzg
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1 Answer

6 votes

Answer:

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

User Dudung
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