Home
Class 12
MATHS
If y= A sin x + B cos x, then prove that...

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

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise NCERT Exemplar Problems and Solution (Short Answer Type Questions)|156 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise NCERT Exemplar Problems and Solution (Long Answer Type Questions)|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|100 Videos

  • BOARD'S QUESTION PAPER MARCH - 2020

    KUMAR PRAKASHAN|Exercise PART - B (Section - C)|4 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Practice Paper-4 (Section-D)|2 Videos

Similar Questions

Explore conceptually related problems

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

(d^(2)y)/(dx^(2)) = cos3x + sin 3x

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

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

If y= sin^(-1)x then prove that (1-x^(2))(d^(2)y)/(dx^(2))-x (dy)/(dx)=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= 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 y= x log ((x)/(a + bx)) prove that (d^(2)y)/(dx^(2)) = (1)/(x) ((a)/(a+ bx))^(2)

If y= 50e^(10x) + 60e^(-10x) , prove that, (d^(2) y)/( dx^(2) ) = 100y .

KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Textbook Illustrations for Practice Work
  1. Find (dy)/(dx), if x^((2)/(3)) + y^((2)/(3))= a^((2)/(3))

    Text Solution

    |

  2. Find (d^(2)y)/(dx^(2)), if y= x^(3) + tan x

    Text Solution

    |

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

    Text Solution

    |

  4. If y= 3e^(2x) + 2e^(3x), prove that (d^(2)y)/(dx^(2))-5 (dy)/(dx) + 6y...

    Text Solution

    |

  5. If y= sin^(-1)x, show that (1 -x^(2)) (d^(2)y)/(dx^(2))-x (dy)/(dx)=0

    Text Solution

    |

  6. Verify Rolle's theorem for the function y= x^(2) + 2, a = - 2 and b= 2

    Text Solution

    |

  7. Verify Mean value Theorem for the function f(x)= x^(2) in the interval...

    Text Solution

    |

  8. Differentiate w.r.t x, the following function: (i) sqrt(3x+2) + (1)...

    Text Solution

    |

  9. Differentiate the following w.r.t x. (i) cos^(-1) (sin x) (ii) tan^...

    Text Solution

    |

  10. Find f'(x) if f(x)= (sin x)^(sin x) for all 0 lt x lt pi.

    Text Solution

    |

  11. For a positive constant a find (dy)/(dx), where y= a^(t + (1)/(t)), an...

    Text Solution

    |

  12. Differentiate sin^(2)x w.r.t e^(cos x)

    Text Solution

    |

  13. Examine the continuity of the function f(x)= 2x + 3 " at " x=1

    Text Solution

    |

  14. Prove that the function f(x)= x^(2) is continuous at x=0.

    Text Solution

    |

  15. Discuss the continuity of the function f given by f(x)= |x| " at " x=0...

    Text Solution

    |

  16. Show that f(x)= {(x^(3)+3",",x ne0),(1",",x=0):} is a discontinuous fu...

    Text Solution

    |

  17. Check the points where the constant function f(x)= k is continuous

    Text Solution

    |

  18. Prove that the identity function on real numbers given by f(x)=x is co...

    Text Solution

    |

  19. Is the function defined by f(x)= |x|, a continuous function

    Text Solution

    |

  20. Discuss the continuity of the function f given by f(x)= x^(3) + x^(2)-...

    Text Solution

    |