Page 153 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes Self Assessment

Fill in the blanks:
1. An equation is basically the mathematical manner to portray a ............................... among
two variables.

dy
2. An equation of the form  Py  Q , in which P & Q are functions of x alone or constant
dx
is called a ............................... equation of the first order.

3. To locate one quantity from the other you ............................... the first by some number,
then add a different number to the outcome.
4. Linear differential equation is commonly known as ................................ .

5. On integrating a linear equation of the first order, we get ............................... as required
general solution.
6. If we are concerning with two or more equations, it is enviable to have a systematic
technique of identifying if the system is consistent and to discover all ............................... .
7. In actual physical problems, quantities normally are associated ..............................., so this
equation is very generally utilized.
8. The system is said to be ............................... if it contains a solution.

11.2 Equations Reducible to the Linear (Bernoulli’s Equation)

dy n
(i) An equation of the form  Py  Qy …..(1)
dx
where P and Q are functions of x only or constants known as Bernoulli’s equation. It can
be made linear.
n
Dividing both sides of (1) by y , we have

y  n dy  Py 1 n  Q …..(2)
dx
–n
Putting y = z

So that (1 n )y  n dy  dz .
dx dx

or y  n dy  1 . dz .
dx 1 n dx

Equation (2) becomes
1 dz
 Pz  Q
1 n dx

dz
or  1 n Pz   1 n  .Q …..(3)
dx
which is a linear differential equation with z as the dependent variable.
If n > 1, then we have to add the solution y=0 to the solutions found by means of the technique
illustrated above.

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