A function y ( t ) satisfies the differential equation y ? = y^2 (a) What are th

Q: A function y ( t ) satisfies the differential equation y ? = y^2 (a) What are th

a) Constant solution is y = 0. b) For all values of y as y' = y^2 is always positive expect 0. At 0 its neither increasing nor decreasing. c) No value of y d) The solution shouldnt depend on |y|, if |y| increase, |y| * 0 is still 0. 2) if y( 0 ) = 0. then y = 0 if( y( 0 ) 0 ), y = 1/x

ID: 3286862 • Letter: A

Question

A function y ( t ) satisfies the differential equation y ? = y^2 (a) What are the constant solutions to the equation? (b) For what values of y is y increasing? (c) For what values of y is y decreasing? (d) What happens to a solution y(t) if |y| increases? (e) Use the above to sketch 3 solutions in the same graph, corresponding to 3 initial conditions y(0) = 0, y (0) > 0, y(0)<0 Please explain out solutions thoroughly I really want to learn how to solve future equations like this myself. Thank you very much in advance, your help is greatly appreciated

Explanation / Answer

a) Constant solution is y = 0.

b) For all values of y as y' = y^2 is always positive expect 0. At 0 its neither increasing nor decreasing.

c) No value of y

d) The solution shouldnt depend on |y|, if |y| increase, |y| * 0 is still 0.

2) if y( 0 ) = 0. then y = 0

if( y( 0 ) < 0 ) y = -1/x and y' = y^2 = 1/x^2

if( y( 0 ) > 0 ), y = 1/x

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A function y ( t ) satisfies the differential equation y ? = y^2 (a) What are th

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