Home
Class 12
MATHS
Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^...

Let `y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R ,` where `f^(prime)(x)` denotes `(dy(x))/(dx),` and `g(x)` is a given non-constant differentiable function on `R` with `g(0)=g(2)=0.` Then the value of `y(2)` is______

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE )|28 Videos
  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos
  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos

Similar Questions

Explore conceptually related problems

Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0)=0,x in R , where f^(prime)(x) denotes (dy(x))/(dx), and g(x) is a given non-constant differentiable function on R with g(0)=g(2)=0. Then the value of y(2) is______

int \ {f(x)*g^(prime)(x)-f^(prime)(x)g(x))/(f(x)*g(x)){logg(x)-logf(x)} \ dx

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

Let x=f(t) and y=g(t), where x and y are twice differentiable function. If f'(0)= g'(0) =f''(0) = 2. g''(0) = 6, then the value of ((d^(2)y)/(dx^(2)))_(t=0) is equal to

If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , write the value of (dy)/(dx) at x=0 .

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)4f(x_0),g^(prime)(x_0)=-7g(x_0), then the value of g^(prime)(1) is ________

If y=|f(x)g(x)h(x)l m n a b c| , prove that (dy)/(dx)=|f^(prime)(x)g^(prime)(x)h^(prime)(x)l m n a b c| .

Let f(x+y)=f(x)+f(y) and f(x)=x^2g(x)AA x,y in R where g(x) is continuous then f'(x) is

If y=f(x)=x^3+x^5 and g is the inverse of f find g^(prime)(2)

If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of lim_(x->a)(g(x)f(a)-g(a)f(x))/(x-a) is (a) -5 (b) 1/5 (c) 5 (d) none of these

VMC MODULES ENGLISH-DIFFERENTIAL EQUATIONS-JEE ADVANCE (ARCHIVE )
  1. Integrating factor of sec^2y dy/dx+x tany=x^3

    Text Solution

    |

  2. Let u(x) and v(x) be two continous functions satisfying the different...

    Text Solution

    |

  3. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

    Text Solution

    |

  4. A curve passes through the point (1,pi/6) . Let the slope of the curve...

    Text Solution

    |

  5. Tangent is drawn at any point P of a curve which passes through (1, 1...

    Text Solution

    |

  6. A spherical rain drop evaporates at a rate proportional to its surf...

    Text Solution

    |

  7. If length of tangent at any point on the curve y=f(x). Intercepted bet...

    Text Solution

    |

  8. A right circular cone with radius R and height H contains a liquid whi...

    Text Solution

    |

  9. A country has a food deficit of 10%. Its population grows continuously...

    Text Solution

    |

  10. A curve passing through the point (1,1) has the porperty that the perp...

    Text Solution

    |

  11. A and B are two separate reservoirs of water. Capacity of reservoir...

    Text Solution

    |

  12. Determine the equation of the curve passing through the origin, in ...

    Text Solution

    |

  13. If y=y(x) satisfies the differential equation 8sqrt(x)(sqrt(9+sqrt(x...

    Text Solution

    |

  14. The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...

    Text Solution

    |

  15. Let y(x) be a solution of the differential equation (1+e^x)y^(prime)+y...

    Text Solution

    |

  16. Consider the family of all circles whose centers lie on the straight l...

    Text Solution

    |

  17. "Let "f:(0.oo)rarrR" be a differentiable function such that "f'(x)=2-...

    Text Solution

    |

  18. Let f:R to R be a differentiable function with f(0)=0. If y=f(x) satis...

    Text Solution

    |

  19. A solution curve of the differential equation (x^(2)+xy+4x+2y+4)(dy)/(...

    Text Solution

    |

  20. let T denote a curve y=f(x) which is in the first quadrant and let the...

    Text Solution

    |