Sketch slope eld for y y2SolutionSolution y y2 Here the righ

Sketch slope eld for y\'= y^2.

Solution:

y\'= y²

Here, the right-hand side of the differential equation depends only on the dependent variable y, not on the independent variable x. Such a differential equation is called autonomous.

Autonomous differential equations are always separable.

Autonomous differential equations have a very special property , their slope fields are horizontal-shift-invariant, i.e. along a horizontal line the slope does not vary.

slope field is given below:

$Sketch slope eld for y\'= y^2.SolutionSolution: y\'= y2 Here, the right-hand side of the differential equation depends only on the dependent variable y, not on$

Sketch slope eld for y y2SolutionSolution y y2 Here the righ

Solution

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