Consider the autonomous differential equation. y/ = (y – 1)(3 – y)² Sketch solutions curves in the t – y plane corresponding to the following initial conditions. Make sure you label your graph and label any equilibrium solutions. y(0) = 4 y(0) = 3 y(0) = 2 y(0) = 1 y(0) = 0. %3D

Q: y′=y,y(0)=1

A: Use dy/dx in place of y'Then separate the variables.

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Q: 3. Solve each equation. y(0) = 1, y' (0) = -1 (a) y" + 4y = 0, (b) y" + 5y = 0

A: We have to solve given problem:

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Q: (2.) Find the general solution to y' + 2ty = 5t.

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Q: ; v' = v ]n(y + 2).

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A: I have explained everything within the solution, Please go through that.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.