Advertisements
Advertisements
Question
Find the differential equation of the family of all straight lines passing through the origin
Solution
The general equation for a family of lines passing through the origin is
y = mx .........(1)
Differentiating w.r.t x,
`("d"y)/("d"x)` = m .......(2)
Using (2) in (1)
y = `(("d"y)/("d"x)) x` is the required differential equation
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:
`("d"^3y)/("d"x^3) = 0`
Find the order and degree of the following diff erential equation:
(2 – y”)2 = y”2 + 2y’
Find the differential equation of the following:
y = cx + c – c3
Find the differential equation of the following:
y = c(x – c)2
Form the differential equation by eliminating α and β from (x – α)2 + (y – β)2 = r2
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
Choose the correct alternative:
Th e differential equation `(("d"x)/("d"y))^3 + 2y^(1/2) = x` is
Choose the correct alternative:
The differential equation formed by eliminating a and b from y = aex + be-x is
Solve yx2dx + e–x dy = 0
