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), 

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  1^st  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 2^nd 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 = Ae^x + Be^3x for different values of A and B.

Solution:         y = A e^x + Be^3x                                    . . . . (1)

                        y₁ = Ae^x + 3Be^3x                                 . . .  (2)   

                        y₂ = Ae^x + 9B^3x                                   . . .  (3) 

                        By eliminating A and B  from the  above  3, we get

                        => 3y + 4y₁ - 4y₂ = 0 => 

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