Question

b) Find the exact solution = () to the differential equation given (0) = 1, and state thethe domain of the function.

Answer 1

Given:

`(dy)/(dx)=2yx+yx^2`

Find: the exact solution y=f(x) to the differential equation, f(0)=1 and domain of the function.

Step-by-step explanation:

`\begin{gathered} dy=(2yx+yx^2)dx \\ dy=y(2x+x^2)dx \\ (dy)/(y)=2xdx+x^2dx \\ \end{gathered}`

on integrating both side,

`logy=x^2+(x^3)/(3)+c`

put f(0)=1,

`\begin{gathered} log1=0^2+(0^3)/(3)+c \\ c=0 \end{gathered}`
`logy=x^2+(x^3)/(3)`