Homogeneous Differential Equations: Solved Example Problems

Example 4.15

Solve the differential equation y2 dx + ( xy + x2 )dy = 0

Solution

Example 4.17

Find the particular solution of the differential equation x 2 dy + y ( x + y) dx = 0 given that x = 1, y = 1

Solution:

Example 4.18

If the marginal cost of producing x shoes is given by (3xy + y2 ) dx + (x 2 + xy) dy = 0 and the total cost of producing a pair of shoes is given by ₹12. Then find the total cost function.

Solution:

Given marginal cost function is (x2 + xy) dy + (3xy + y2)dx=0

Example 4.19

The marginal revenue ‘y’ of output ‘q’ is given by the equation . Find the total Revenue function when output is 1 unit and Revenue is ₹5.

Solution: