Formation of differential Equation:
We know y2 = 4ax is a parabola whose vertex is origin and axis as the x-axis . If a is a parameter, it represents a family of parabola with the vertex at (0, 0) and axis as y = 0 .
Differentiating y2 = 4ax . . (1)
. . (2)
From equation (1) and (2), ![2381_Order and Degree of a Differential Equation5.png](https://www.expertsmind.com/../CMSImages/2381_Order and Degree of a Differential Equation5.png)
This is a differential equation for all the members of family and it does not contain any parameter .
(i) The differential equation of a family of curves of one parameter is the differential equation of the 1st order, which is obtained by eliminating the parameter by differentiation.
(ii) The differential equation of a family of curves of 2 parameter is a differential equation of the 2nd order, which can be obtained by eliminating the parameter by differentiating the algebraic equation twice. Similar process is used to find out differential equation of a family of curves of 3 or more parameter.
Example Find differential equation of the family of curves y = Aex + Be3x for different values of A and B.
Solution: y = A ex + Be3x . . . . (1)
y1 = Aex + 3Be3x . . . (2) ![534_Order and Degree of a Differential Equation6.png](https://www.expertsmind.com/../CMSImages/534_Order and Degree of a Differential Equation6.png)
y2 = Aex + 9B3x . . . (3) ![2251_Order and Degree of a Differential Equation7.png](https://www.expertsmind.com/../CMSImages/2251_Order and Degree of a Differential Equation7.png)
By eliminating A and B from the above 3, we get
=> 3y + 4y1 - 4y2 = 0 => ![883_Order and Degree of a Differential Equation9.png](https://www.expertsmind.com/../CMSImages/883_Order and Degree of a Differential Equation9.png)
Email based Formation of differential Equation Assignment Help - Homework Help
We at www.expertsmind.com offer email based Formation of differential Equation assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.
Expertsmind's best education services
- Quality assignment-homework help assistance 24x7 hrs
- Best qualified tutor's network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work