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Differential equations and related rates — Question 221

Original QCE Vault practice · 6 marks

Q221 · Practice questionTechnology-freeComplex unfamiliar6 marks

QUESTION 221 (6 marks)

Consider

dy/dt=\sqrt y

, y nonnegative, with y(0)=0.

Immediate solution y=t squared/4 and an example delayed solution starting at t=2. The delayed solution is zero before t=2.

a)

Verify that both

y=0

and

y=t^2/4

for

t\ge0

satisfy the initial-value problem.

[2 marks]

b)

For

c\ge0

, verify the delayed solution:

y=0

on

0\le t\le c

and

y=(t-c)^2/4

for t>c.

[3 marks]

c)

Explain what is lost if separation immediately divides by

\sqrt y

.

[1 mark]

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