Advertisements
Advertisements
Question
Find the differential equation of the following:
x2 + y2 = a2
Advertisements
Solution
Differentiating w.r. to x
`2x + 2y ("d")/("d"x)` = 0
⇒ `2y ("d"y)/("d"x) = - 2x`
`("d"y)/("d"x) = (-2x)/(2y)`
⇒ `("d"y)/("d"x) = (-x)/y`
`y ("d"y)/("d"x) = -x`
⇒ `x + y ("d"y)/("d"x)` = 0
APPEARS IN
RELATED QUESTIONS
Find the order and degree of the following differential equation:
`("d"^2y)/("d"x^2) = sqrt(y - ("d"y)/("d"x))`
Find the order and degree of the following differential equation:
(2 – y”)2 = y”2 + 2y’
Find the differential equation of the following:
xy = c2
Form the differential equation by eliminating α and β from (x – α)2 + (y – β)2 = r2
Find the differential equation of the family of all straight lines passing through the origin
Form the differential equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x-axis
Find the differential equation of the family of a parabola with foci at the origin and axis along the x-axis
Choose the correct alternative:
The degree of the differential equation `("d"^4y)/("d"x^4) - (("d"^2y)/("d"x^2))^4 + ("d"y)/("d"x) = 3`
Choose the correct alternative:
The differential equation formed by eliminating a and b from y = aex + be-x is
The differential equation whose solution is Ax2 + By2 = 1 where A and B are arbitrary constants is of ______.
