5. (Refer to Exercise 2) A differential equation (see Exercise 2 above) and various initial conditions are specified. Sketch the graphs of the solutions satisfying these initial conditions. Put all your graphs on one pair of axes! (i) y(0) = 1, (ii) y(1) = 0, (iii) y(0) = 6, (iv) y(0) = 4.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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please solve question number five, refer to the solved solution 

5. (Refer to Exercise 2) A differential equation (see Exercise 2 above) and various initial conditions are specified. Sketch
the graphs of the solutions satisfying these initial conditions. Put all your graphs on one pair of axes!
(i) y(0) = 1,
(ii) y(1) = 0,
(iii) y(0) = 6,
(iv) y(0) = 4.
Transcribed Image Text:5. (Refer to Exercise 2) A differential equation (see Exercise 2 above) and various initial conditions are specified. Sketch the graphs of the solutions satisfying these initial conditions. Put all your graphs on one pair of axes! (i) y(0) = 1, (ii) y(1) = 0, (iii) y(0) = 6, (iv) y(0) = 4.
The given differential equation is
dy
y2 – 4y – 12
dt
First, draw the slope field of the given
differential equation satisfying the initial
condition «1)= 0. It is a particular solution curve
that passes through the point (1,0), The slope field
is sketched below.
--
A(1, Q)
Transcribed Image Text:The given differential equation is dy y2 – 4y – 12 dt First, draw the slope field of the given differential equation satisfying the initial condition «1)= 0. It is a particular solution curve that passes through the point (1,0), The slope field is sketched below. -- A(1, Q)
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