# prob9 - ∞ will be considered to be an end-point 1 12 a...

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Math 151 Spring 2007 Problem Set # 9 Separable Di f erential Equations Starred Problems are due on Monday, March 24 In problems 1-9, a) Determine the general solution of the given di f erential equation, b) Determine the solution of the solution of the equation that corresponds to the given initial condition. 1 . dy dx = y 2 ,y (0) = 1 . 2* . dy dx = y 2 +1 ,y ³ π 4 ´ =0 . 3 . dy dx = p 1+ y 2 ,y (0) = 2 4*. dy dx + y 2 sin ( x )=0 ,y ³ π 3 ´ = 1 2 5. dy dx = 1+ y 2 1+ x 2 ,y (0) = 1 6*. dy dx = y 2 x ,y ¡ e 2 ¢ =2 7. dy dx = 2 xy 2 1+ x 2 ,y (0) = 2 8*. dy dx = y 2 1+ x 2 ,y (1) = 2 π 9 . dy dt =s in( t ) y 2 ,y ( π )=4 10* . a) Determine the steady-state solutions of the di f erential equation dy dt = 1 4 y ( t ) 1 100 y 2 ( t ) . b) Find the solution f of the initial value problem dy dt = 1 4 y ( t ) 1 100 y 2 ( t ) ,y (0) = 5 . c) Determine lim t →−∞ f ( t ) and lim t + f ( t ) . 11 . a) Find the solution f of the initial value problem dy dt = 1 4 y ( t ) 1 100 y 2 ( t ) ,y (0) = 50 . Specify the domain of f . b) Determine the appropriate limits of f at the end-points of its domain (

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Unformatted text preview: ∞ will be considered to be an end-point). 1 12 . a) Find the solution f of the initial value problem dy dt = 1 4 y ( t ) − 1 100 y 2 ( t ) , y (0) = − 50 . Specify the domain of f . b) Determine the appropriate limits of f at the end-points of its domain ( ± ∞ will be considered to be an end-point). 13*. a) Determine the steady-state solutions of the di f erential equation dy dt = 4 − 1 100 y 2 ( t ) . b) Find the solution f of the initial value problem dy dt = 4 − 1 100 y 2 ( t ) , y (0) = 0 . c) Show that lim t →−∞ f ( t ) = − 20 and lim t → + ∞ f ( t ) = 20 . 14 . Find the solution f of the initial value problem dy dt = 4 − 1 100 y 2 ( t ) , y (0) = 40 . Specify the domain of f. 2...
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prob9 - ∞ will be considered to be an end-point 1 12 a...

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