Solution of differential equation:
The general solution of the differential equation is the relation in the variables x, y obtained by integrating (by removing derivatives) where relation contains as many arbitrary constants as the order of equation. The general solution of differential equation of the 1st order contains one arbitrary constant while that of the 2nd order contains 2 arbitrary constants. In general solution, if particular values of arbitrary constant are put, we get a particular solution which will give one member of family of curves.
To solve the differential equation of the 1st order and the 1st degree:
Simple standard form of the differential equation of 1st order and 1st degree are as follows:
(i) Variable Separable
Form f(x) dx + Φ(y) dy = 0
Method: Integrate it that is, find ∫f(x) dx + ∫Φ(y)dy = c
Example : Solve
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Solution: Given ![575_Solution of differential equation1.png](https://www.expertsmind.com/../CMSImages/575_Solution of differential equation1.png)
![2100_Solution of differential equation2.png](https://www.expertsmind.com/CMSImages/2100_Solution%20of%20differential%20equation2.png)
Integrating, we get ln y - ex =c
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