Home
Class 12
MATHS
If y=3e^(2x)+2e^(3x) , prove that (d^2y)...

If `y=3e^(2x)+2e^(3x)` , prove that `(d^2y)/(dx^2)-5(dy)/(dx)+6y=0` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If y=3e^(2x)+2e^(3x), prove that (d^(2)y)/(dx^(2))-5(dy)/(dx)+6y=0

If y=3e^(2x)+2e^(3x) Prove that (d^(2)y)/(dx^(2))-5(dy)/(dx)+6y=0

If y= 3e^(2x)+ 2e^(3x) ,then (d^(2)y)/(dx^(2))-5(dy)/(dx) =

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

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

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

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

If y=a+(b)/(x) ; prove that x(d^(2)y)/(dx^(2))+2(dy)/(dx)=0

If y= x^(2) e^(x) ,then ( d^(2)y)/(dx^(2)) -(dy)/(dx) =

BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If x=sqrt(a^sin^((-1)t)) , y=sqrt(a^cos^((-1)t)) , show that (dy)/(...

    Text Solution

    |

  2. If y = x^3 + tan x, show that (d^2y)/dx^2= 6x + 2 sec^2 tanx.

    Text Solution

    |

  3. If y=3e^(2x)+2e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

    Text Solution

    |

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

    Text Solution

    |

  5. If y=5cosx-3sinx , prove that (d^2y)/(dx^2)+y=0 .

    Text Solution

    |

  6. If y=3cos(logx)+4sin(logx) , show that x^2y2+x y1+y=0

    Text Solution

    |

  7. If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...

    Text Solution

    |

  8. If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

    Text Solution

    |

  9. If y=(tan^(-1)x)^2 , show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

    Text Solution

    |

  10. For a positive constant a find (dy)/(dx) , where y=a^(t+1/t) and x=(t+...

    Text Solution

    |

  11. Differentiate sin^2x w.r.t. e^(cosx) .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((x+1)^2)

    Text Solution

    |

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

    Text Solution

    |

  16. If x=a(cost+tsint) and y=a(sint- tcost) , find (d^2y)/(dx^2) .

    Text Solution

    |

  17. If y=e^acos^((-1)x) , -1lt=xlt=1 , show that (1-x^2) (d^2y)/(dx^2)-x(d...

    Text Solution

    |

  18. If y=|sinxcosxsinxcosx-sinxcosxx1 1| , find (dy)/(dx) .

    Text Solution

    |

  19. if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2)...

    Text Solution

    |

  20. If (1+x)^n=C0+C1+C2\ x^2+\ dot+Cn\ x^n , using derivatives prove th...

    Text Solution

    |