Home
Class 12
MATHS
x^((1)/(2))((d^(2)y)/(dx^(2)))^((1)/(3))...

`x^((1)/(2))((d^(2)y)/(dx^(2)))^((1)/(3)) +x.(dy)/(dx)+y=0` has order 2 and degree 1. Prove.

Text Solution

Verified by Experts

The correct Answer is:
The order of the equation is 2 and its degree is 1.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE- 8(a)|15 Videos
  • DIFFERENTIAL EQUATIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE- 8(b)|17 Videos
  • DEFINITE INTEGRALS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Long Answer Question|3 Videos
  • ELLIPSE

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE 4(B)|15 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are the degrees of the differential equation (d^(2)y)/(dx^(2)) - (5dy)/(dx) + 6y = 0, ((dy)/(dx))^(3) + ((dy)/(dx))^(2) + y^(4) = 0, ((d^(3)y)/(dx^(3)))^(2) + 2 ((dy)/(dx))^(4) + (dy)/(dx) = cos x then the ascending order of a, b, c is

Find the order and degree of the following D.E's (i) (d^(2)y)/(dx^(2)) + 2((dy)/(dx))^(2) + 5y = 0 (ii) 2(d^(2)y)/(dx^(2)) = (5+(dy)/(dx))^((5)/(3)) (iii) 1+((d^(2)y)/(dx^(2)))^(2) = [2+((dy)/(dx))^(2)]^((3//2)) (iv) [(d^(2)y)/(dx^(2))+((dy)/(dx))^(3)]^((6/(5)) = 6y (v) [((dy)/(dx))^(2) + (d^(2)y)/(dx^(2))]^((7)/(3)) = (d^(3y))/(dx^(3)) (vi) [((dy)/(dx))^((1)/(2)) + ((d^(2)y)/(dx^(2)))^((1)/(2))]^((1)/(4)) = 0 (vii) (d^(2)y)/(dx^(2)) + p^(2)y = 0 (viii) ((d^(3)y)/(dx^(3)))^(2) -3((dy)/(dx))^(2) - e^(x) = 4

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

If (x ^(2))/(a ^(2)) - (y ^(2))/(b ^(2)) =1 then (dy)/(dx)=

Find the order and degree, if defined, of each of the following differential equations: (i) (dy)/(dx) - cos x = 0 (ii) xy (d^(2)y)/(dx^(2)) + x((dy)/(dx))^(2) - y (dy)/(dx) = 0 (iii) y''' + y^(2) + e^(y)' = 0

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

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DIFFERENTIAL EQUATIONS -EXERCISE- 8(e)
  1. x^((1)/(2))((d^(2)y)/(dx^(2)))^((1)/(3)) +x.(dy)/(dx)+y=0 has order 2 ...

    Text Solution

    |

  2. Find the I.F. of the following differential equations by transforming ...

    Text Solution

    |

  3. Find the I.F. of the following differential equations by transforming ...

    Text Solution

    |

  4. Solve the following differential equations. (dy)/(dx)+y tan x=cos^(3...

    Text Solution

    |

  5. Solve the following differential equations. (dy)/(dx)+y sec x=tan x

    Text Solution

    |

  6. Solve the following differential equations. (dy)/(dx)-y tan x =e^(x)...

    Text Solution

    |

  7. Solve the following differential equations. x (dy)/(dx) + 2y=log x

    Text Solution

    |

  8. Solve the following differential equations. (1+x^(2))(dy)/(dx)+y=e^(t...

    Text Solution

    |

  9. Solve the following differential equations. (dy)/(dx)+(2y)/(x)=2x^(2...

    Text Solution

    |

  10. Solve the following differential equations. (dy)/(dx)+(4x)/(1+x^(2))y...

    Text Solution

    |

  11. Solve the following differential equations. x(dy)/(dx)+y=(1+x)e^(x)

    Text Solution

    |

  12. Solve the following differential equations. (dy)/(dx)+(3x^(2))/(1+x...

    Text Solution

    |

  13. Solve the following differential equations. (dy)/(dx)-y=-2e^(-x)

    Text Solution

    |

  14. Solve the following differential equations. (1+x^(2))(dy)/(dx)+y=ta...

    Text Solution

    |

  15. Solve the following differential equations. (dy)/(dx)+y tan x=sin x

    Text Solution

    |

  16. Solve the following differential equations. cos x. (dy)/(dx)+y sin x...

    Text Solution

    |

  17. Solve the following differential equations. sec x. dy= (y + sin x)dx

    Text Solution

    |

  18. Solve the following differential equations. x log x. (dy)/(dx)+y=2 l...

    Text Solution

    |

  19. Solve the following differential equations. (x+y+1)(dy)/(dx)=1

    Text Solution

    |

  20. Solve the following differential equations. x(x-1)(dy)/(dx)-y=x^(3)(...

    Text Solution

    |

  21. Solve the following differential equations. (x+2y^(3))(dy)/(dx)=y

    Text Solution

    |