Home
Class 12
MATHS
If y=" "A" "s in" "x+" "B" "cos" "x , th...

If `y=" "A" "s in" "x+" "B" "cos" "x` , then prove that `(d^2y)/(dx^2)+y=0` .

Text Solution

Verified by Experts

The correct Answer is:
`(d^(2)y)/(dx^(2))+y=0`.
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXAMPLES|9 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT GUJARATI|Exercise EXERCISE 5.1|39 Videos

  • APPLICATION OF INTEGRALS

    NCERT GUJARATI|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NCERT GUJARATI|Exercise Miscellaneous Exercises on Chapter 4|18 Videos

Similar Questions

Explore conceptually related problems

If y= A sin x + B cos x , then prove that (d^(2)y)/(dx^(2)) +y= 0

If y=5 cos x-3 sin x , prove that (d^(2)y)/(dx^(2)) + y= 0

If x = a cos theta + b sin theta and y =asin theta-b cos theta , then prove that y^2 (d^2y)/(dx^2)-x(dy)/(dx)+y=0

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

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

If x sin (a + y) + sin a cos (a + y)= 0 , then prove that (dy)/(dx)= (sin^(2) (a + y))/(sin a)

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

If y=xlog(x/(a+bx)) , then prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

If cos y= x cos (a + y) , with cos a ne +- 1 , prove that (dy)/(dx) = (cos^(2) (a + y))/(sin a)

NCERT GUJARATI-CONTINUITY AND DIFFERENTIABILITY-MISCELLANEOUS EXERCISE ON CHAPTER 5
  1. If y=" "A" "s in" "x+" "B" "cos" "x , then prove that (d^2y)/(dx^2)...

    Text Solution

    |

  2. Differentiate w.r.t.x the function in Exercises 1 to 11. (3x^(2)-9x+...

    Text Solution

    |

  3. Differentiate w.r.t. x the functionsin^3x+cos^6x

    Text Solution

    |

  4. Differentiate w.r.t. x the function(5x)^(3cos2x).

    Text Solution

    |

  5. sin^(-1)(xsqrt(x)),0 le x le 1

    Text Solution

    |

  6. Differentiate w.r.t.x the function in Exercises 1 to 11. (cos^(-1)""...

    Text Solution

    |

  7. cot^-1{sqrt(1+sinx)+sqrt(1-sinx)}/{sqrt(1+sinx)-sqrt(1-sinx)}

    Text Solution

    |

  8. Differentiate w.r.t. x the function(logx)^(logx), x >1

    Text Solution

    |

  9. Differentiate w.r.t.x the function in Exercises 1 to 11. cos( a cos ...

    Text Solution

    |

  10. (sinx-cosx)^((sinx-cosx)),(pi)/(4) ltx lt (3pi)/(4)

    Text Solution

    |

  11. Differentiate w.r.t.x the function in Exercises 1 to 11. x^(x)+x^(a)...

    Text Solution

    |

  12. x^(x^(2)-3)+(x-3)^(x^2)," for "x gt 3.

    Text Solution

    |

  13. Find (dy)/(dx),if y=12(1-cost), x=10(t-sint),-pi/2<t<pi/2

    Text Solution

    |

  14. Find (dy)/(dx), if y=sin^(-1)x+sin^(-1)sqrt(1-x^2),-1lt=xlt=1.

    Text Solution

    |

  15. xsqrt(1+y)+ysqrt(1+x)=0, then (dy)/(dx)=

    Text Solution

    |

  16. If (x-a)^2+(y-b)^2=c^2, for some c > 0, prove that ([1+((dy)/(dx))^2]^...

    Text Solution

    |

  17. If cosy=xcos(a+y) , with cosa!=+-1 , prove that (dy)/(dx)=(cos^2(a+y))...

    Text Solution

    |

  18. If x=a(cos t+t\ s in\ t) and y=a\ (sint-t\ cos t),\ \ then find (d^2\...

    Text Solution

    |

  19. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

    Text Solution

    |

  20. Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all...

    Text Solution

    |

  21. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

    Text Solution

    |