Home
Class 12
MATHS
If x(dy)/(x t)=x^2+y-2,y(1)=1, then y(2)...

If `x(dy)/(x t)=x^2+y-2,y(1)=1,` then `y(2)` equal________

Text Solution

Verified by Experts

The correct Answer is:
2
Given, `(dy)/(dx)-1/xy=(x-2/x)`
I.F. `=e^(-int1/xdx)=e^(-"ln x"=1/x)`
Now, general solution is given by
`y/x= int(x-2/x)1/xdx` or `y=x^(2)-2x+2`
Hence, `y(2) =(2)^(2)-2x+2`
Hence, `y(2)=(2)^(2)-2(2)+2=2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise JEE Main Previous Year|12 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|12 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Matrix Match Type|3 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

If x(dy)/(dx)=x^(2)+y-2, y(1)=1 , then y(2) equals ………………..

If y = y(x) is the solution of the differential equation, x dy/dx+2y=x^2 satisfying y(1) = 1, then y(1/2) is equal to

if y=y(x) and (2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1, then y(pi/2)=

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

Let y be an implicit function of x defined by x^(2x)-2x^xcot y-1=0. Then y '(1) equals: 1 b. log2 c. -log2 d. -1

Let y = y(x) be the solution of the differential equation x dy/dx+y=xlog_ex,(xgt1)." If " 2y(2)=log_e4-1," then "y(e) is equal to

If y=(1-x)^(2)/x^(2), " then " (dy)/(dx)= is

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

If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to x/y (b) y/(x^2) (x^2-y^2)/(x^2+y^2) (d) y/x

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