Question

State whether the following statements are true or false. Justify your answers with the

help of a short proof or a counter-example. (10)

i) n

y′ + P(x) y = Q(x) y is a linear equation for integral values of n.

ii) ,0 y = is a singular solution of the differential equation 27 8 .0

3

 =











−

dx

dy

y

iii) 2 4

1

xy + y

is an integrating factor for the differential equation

( ) ( ) .0

2 2 3 3

x y + y dx + y − x dy =

iv) Equation 2 2

x ( y − px) = yp is reducible to clairaut’s form.

v) x

2 is a particular integral for . e 2

x

y′ − y = e​

Answer 1

Answer:

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