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Maths: Differential Equations: First order and first degree differential: Solved Example Problems

First order and first degree differential

Example 4.6

Solve: ( x2 + x +1) dx + ( y2 - y + 3)dy = 0

*Solution:*

Example 4.12

The marginal cost function of manufacturing *x* gloves is 6 + 10*x* − 6*x*2 . The total cost of producing a pair of gloves is ₹100. Find the total and average cost function.

*Solution:*

Example 4.13

The normal lines to a given curve at each point ( *x*, *y*) on the curve pass through the point (1,0). The curve passes through the point (1,2). Formulate the differential equation representing the problem and hence find the equation of the curve.

*Solution:*

Example 4.14

The sum of ₹2,000 is compounded continuously, the nominal rate of interest being 5% per annum. In how many years will the amount be double the original principal? (log*e* 2 = 0.6931)

*Solution:*

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12th Business Maths and Statistics : Chapter 4 : Differential Equations : First order and first degree differential: Solved Example Problems | with Answer, Solution, Formula | Differential Equations

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