Home
Class 12
MATHS
The solution of ((dy)/(dx))^(2)-2(x+(1)/...

The solution of `((dy)/(dx))^(2)-2(x+(1)/(4x))(dy)/(dx)+1=0`

A

`y = x^(2) + c`

B

`y = (1)/(2) In (x) + c, x gt 0`

C

`y = (x)/(2) + c`

D

`y = (x^(2))/(2) + c`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`rArr" "((dy)/(dx))^(2)-3(x+(1)/(4x))(dy)/(dx)+1 = 0`
`rArr" "((dy)/(dx)-2x)((dy)/(dx)-(1)/(2x))=0`
`therefore" "dy = 2x dx or dy=(1)/(2x)dx`
`rArr" "y=x^(2)+ c or y = (1)/(2)"In x"+c, x gt 0`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Comprehension Type|2 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Single Correct Answer Type|37 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

The solution of (dy)/(dx)=2^(y-x) is

The solution of (dy)/(dx)+p(x)y=0 is

The solution of (dy)/(dx)+1/(x^(2)+1)= 0 is

Solution of (dy)/(dx)+2x y=y is

The solution of (1+x)(dy)/(dx)+1=e^(x-y) is

The solution of (x^2dy)/(dx)-x y=1+cos(y/x) is

(1+x^(2))(dy)/(dx) = 1-y

(1-x^(2))(dy)/(dx)-xy=1