Home
Class 12
MATHS
If y=y(x) and it follows the relation...

If `y=y(x)` and it follows the relation `4x e^(x y)=y+5sin^2x ,` then `y^(prime)(0)` is equal to______

Text Solution

Verified by Experts

The correct Answer is:
4
We have `4xe^(xy)=y+5sin^(2)x`………….(1)
Putting x=0, in equation (1), we get y=0.
Therefore, (0,0) lies on the curve.
Now, on differentiating equation (1) w.r.t. x, we get
`4e^(xy)+4xe^(xy)(x(dy)/(dx)+y)=(dy)/(dx)+10sinxcosx`
or `y^(')(0)=4`
Doubtnut Promotions Banner Mobile Dark
|

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 y = y(x) and it follows the relation e^(xy) + y cos x = 2 , then find (i) y'(0) and (ii) y"(0) .

If the equation 2x^2+4x y+7y^2-12 x-2y+t=0,w h e r et is a parameter has exactly one real solution of hte form (x ,y) , then hte sum of (x+y) is equal to ______.

y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)) , AAx,y->R and f'(0)=0.Then f(6)is equal ______

If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then

Solve the differential equation y e^(x)/(y) dx = (x e^(x)/(y) + y^(2))dy ( y ne 0) .

Solve the following differential equations: (e^(y) +1) cos x dx +e^(y) sin x dy =0

Find the image of the circle x^2+y^2-2x+4y-4=0 in the line 2x-3y+5=0

If A={(x,y)/y=e^x.x in [0,oo)} and B={(x,y)/y=sinx, x in [0,oo)} then n(AcapB) is?

If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to

If y=e^(tan^(-1)x) , show that (1+x^(2))y''+(2x-1)y'=0 .

Home
Profile