For the following autonomous ODEs, find the equilibrium solutions, then classify each solution as stable/unstable etc. Finally, sketch a diagram depicting the equilibrium solution along with several possible integral curves. (a) y' = y² (y² - 1) (b) y'= y(1 - y²) (c) y' = y²(1 - y)²

Q: y′=y,y(0)=1

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

Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: Find the solution for following variable separable equation: x² (dx/dy) = y - xy , y(1)=1

A: The main objective is to solve the given variable separable equation.

Q: If the equilibrium of dy/dx = y - sqrt(y) when y>0 is y=1, is it a stable or unstable equilibrium?

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Q: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: Consider the following equation: x?y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 1. Verify that y, (x) = x…

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Q: Find y as a function of a if y" − 3y" − y + 3y = 0, y(0) = −9, y'(0) = −8, y'(0) = 7. y(x) =

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Q: Copy the slope fields (mentioned in the Attachment) and sketch in some of the solution curves. y' =…

A: Given: y'=y(y+1)(y-1)

Q: V3 (9) 1 x' x(0) = V3 - 1

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Q: Use the convolution to write a formula for problem: y" – 3y' + 2y = f(t), y(0) = 1, y'(0) = 0; -

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Q: Graph the slope field for the equation dx/dy = -x(x2-4) and attach it to the solution. Draw (by hand…

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