Students can download 12th Business Maths Chapter 4 Differential Equations Miscellaneous Problems and Answers, Samacheer Kalvi 12th Business Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems

Question 1.
Suppose that Qd = 30 – 5P + 2 \(\frac{d p}{d t}+\frac{d^{2} p}{d t^{2}}\) and Qs = 6 + 3P. Find the equilibrium price for market clearance.
Solution:
For equilibrium price Qd = Qs
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q1
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q1.1

Question 2.
Form the differential equation having for its general solution y = ax2 + bx
Solution:
Given y = ax2 + bx
Since there are 2 constants a, b we have to differentiate twice to eliminate them
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q2
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q2.1

Question 3.
Solve yx2 dx + e-x dy = 0
Solution:
The given equation can be written as
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q3

Question 4.
Solve: (x2 + y2) dx + 2xy dy = 0
Solution:
The given equation can be written as \(\frac{d y}{d x}=-\frac{\left(x^{2}+y^{2}\right)}{2 x y}\)
It is a homogeneous differential equation
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q4
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q4.1
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q4.2

Question 5.
Solve: x \(\frac{d y}{d x}\) + 2y = x4
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q5

Question 6.
A manufacturing company has found that the cost C of operating and maintaining the equipment is related to the length ‘m’ of intervals between overhauls by the equation \(m^{2} \frac{d C}{d m}\) + 2mC = 2 and c = 4 and when m = 2. Find the relationship between C and m.
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q6
given that c = 4 when m = 2
4(4) = 2(2) + k
k = 12
So the relation ship between C and m is Cm2 = 2m + 12 = 2(m + 6)

Question 7.
Solve (D2 – 3D + 2)y = e4x given y = 0 when x = 0 and x = 1.
Solution:
(D2 – 3D + 2)y = e4x
The auxiliary equations is m2 – 3m + 2 = 0
(m – 2) (m – 1) = 0
m = 2, 1
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q7
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q7.1
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q7.2

Question 8.
Solve: \(\frac{d y}{d x}\) + y cos x = 2cos x
Solution:
The given equation can be written as \(\frac{d y}{d x}\) + (cos x)y = 2 cos x
It is of the form \(\frac{d y}{d x}\) + Py = Q
Where P = cos x, Q = 2 cos x
Now ∫Pdx = ∫cos x dx = sin x
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q8

Question 9.
Solve: x2y dx – (x3 + y3) dy = 0
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q9
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q9.1

Question 10.
Solve: \(\frac{d y}{d x}\) = xy + x + y + 1
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 4 Differential Equations Miscellaneous Problems Q10

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