Linearizing a Non Linear Differential Eq

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Homework Statement



Use a suitable substitution to transform the nonlinear DE (dy)/(dx)+y=y² into a linear equation in the new variable z.
and
without solving the DE, justify the possible methods that can be used to solve the DE found in first part.

Homework Equations



I have no idea what to do in order to solve this.

The Attempt at a Solution



dy/dx=y2 -y
dy/dx= y(y-1)

∫dy/y=∫(y-1)dx

ln(y)=y-1??

eln(y)=e(y-1)

y= ey-1 I don't think this is write, but this is what I have... can someone help?
 
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Did you not understand the problem? Surely you saw the "without solving the DE" part?

(And "\int y-1 dx", where y is an unknown function of x, is certainly not "y- 1". If you do not know y as a function of x, you cannot integrate with respect to x. If you wanted to solve the equation, you should instead completely separate "x" and "y":
\int \frac{dy}{y(y-1)}= \int dx
using "partial fractions" on the left.)
 
HallsofIvy said:
Did you not understand the problem? Surely you saw the "without solving the DE" part?

(And "\int y-1 dx", where y is an unknown function of x, is certainly not "y- 1". If you do not know y as a function of x, you cannot integrate with respect to x. If you wanted to solve the equation, you should instead completely separate "x" and "y":
\int \frac{dy}{y(y-1)}= \int dx
using "partial fractions" on the left.)

Sorry I might have written the questions wrong, first part is separate from the second part.
The questions below are the right ones

3a.Use a suitable substitution to transform the nonlinear DE (dy)/(dx)+y=y² into a linear equation in the new variable z.
3b.without solving the DE, justify the possible methods that can be used to solve the DE found in 3a.
 
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