Home
Class 12
MATHS
If y="sin"(sinx),"prove that" (d^2y)/...

If `y="sin"(sinx),"prove that"` `(d^2y)/(dx^2)+tanx(dy)/(dx)+ycos^2x=0.`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|406 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|232 Videos

Similar Questions

Explore conceptually related problems

If y="sin"(sinx),"p r o v et h a t" (d^2y)/(dx^2)+tanx(dy)/(dx)+ycos^2x=0.

If y=sin(sinx) , prove that (d^2y)/(dx^2)+tanxdot(dy)/(dx)+y\ cos^2x=0 .

If y=sin (sinx) prove that (d^(2)y)/(dx^(2)) + "tan x" (dy)/(dx) + y cos^(2) x =0 .

If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0

If y=cos (sin x) , show that (d^2y)/(dx^2)+tan x""(dy)/(dx)+y cos^2 x=0

If y=sin(logx) , prove that x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

If y=e^x(sin x+cosx) prove that (d^2y)/(dx^2)-2 (dy)/(dx)+2y=0 .

If y=e^x(sinx+cosx) prove that (d^2y)/(dx^2)-2(dy)/(dx)+2y=0 .

If y=x^x , prove that (d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0

If y=x^x , prove that (d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0

RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If x=2cost-cos2t ,y=2sint-sin2t ,"f i n d"(d^2y)/(dx^2)"a t"t=pi/2dot

    Text Solution

    |

  2. If y="log"(1+cosx),"p r o v et h a t"(d^3y)/(dx^3)+(d^2y)/(dx^2)dot(d...

    Text Solution

    |

  3. If y="sin"(sinx),"prove that" (d^2y)/(dx^2)+tanx(dy)/(dx)+ycos^2x=0...

    Text Solution

    |

  4. If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^...

    Text Solution

    |

  5. If x=a(cost+tsint) and y=a(sint-tcost), then find the value of (d^2y)...

    Text Solution

    |

  6. If y=(cot^(-1)x)^2 , prove that y2(x^2+1)^2+2x(x^2+1)y1=2 .

    Text Solution

    |

  7. If y=e^xcosx , prove that (d^2y)/(dx^2)=2\ e^xcos(x+pi/2) .

    Text Solution

    |

  8. If x=cos t + (log tant)/2, y=sin t, then find the value of (d^2y)/(dt^...

    Text Solution

    |

  9. Find A and B so that y=Asin3x+bcos3x satisfies the equation (d^2y)/(d...

    Text Solution

    |

  10. If x=asint-bcost ,y=acost+bsint ,"p r o v et h a t" (d^2y)/(dx^2)=-...

    Text Solution

    |

  11. If y=e^(ex) (ax+b), show that y^2-4y1+4y=0

    Text Solution

    |

  12. If x=asectheta,y=btantheta,"prove that"(d^2y)/(dx^2)=-(b^4)/(a^2y^3)

    Text Solution

    |

  13. If y=e^"tan"^((-1)"x")), prove that (1+x^2)y2+(2x-1)y1=0.

    Text Solution

    |

  14. If y=(sin^(-1)x)^2 ,prove that (1-x^2)y2-x y1-2=0.

    Text Solution

    |

  15. If y={"log"(x+sqrt(x^2+1))}^2,"show that"(1+x^2)(d^2y)/(dx^2)+x(dy)/(...

    Text Solution

    |

  16. If x=sin(1/alogy),"show that"(1-x^2)y2-xy1-a^2y=0.

    Text Solution

    |

  17. If y=x+tan x, show that cos^2 x (d^2y)/(dx^2)-2y+2x=0

    Text Solution

    |

  18. If y=e^-x cos x, show that (d^2y)/(dx^2)= 2e^-x sin x

    Text Solution

    |

  19. If y=log(sinx),"p r o v et h a t"(d^3)/(dx^3)=2cosxcos e c^3xdot

    Text Solution

    |

  20. If y=x^3logx ,"prove that"(d^4y)/(dx^4)=6/xdot

    Text Solution

    |