Q6 of 26 Page 1

Write the differential equation representing the curve y2 = 4ax, where a is an arbitrary constant.

Given: Curve is y2 = 4ax


To find: Differential Equation


Proof:


Taking given curve


y2 = 4ax …(i)


Differentiating both the sides with respect to, we get





Putting the value of 4a in eq. (i), we get






More from this chapter

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4

If , Write the cofactor of a32 (the element of third row and 2nd column).

 5

If m and n are the order and degree, respectively of the differential equation

, then write the value of m+n.


 7

To raise money for an orphanage, students of three schools A, B and C organized an exhibition in their locality, where they sold paper bags, scrap-books and pastel sheets made by them using recycled paper, at the rate of Rs. 20, Rs.15 and Rs. 5 per unit respectively. School A sold 25 paper-bags 12 scrap-books and 34 pastel sheets. School B sold 22 paper-bags, 15 scrapbooks and 28 pastel-sheets while school C sold 26 paper-bags, 18 scrap-books and 36 pastel sheets. Using matrices, find the total amount raised by each school.

By such exhibition, which values are inculcated in the students?


 8

Let , then show that A2 – 4A + 7I = O.

Using this result calculate A3 also.


OR


If , find A-1 , using elementary row operations.