Home
Class 12
MATHS
the solution of the differential equatio...

the solution of the differential equation `(dy)/(dx)+(x(x^(2)+3y^(2))/(y(y^(2)+3x^(2)))=0` is

A

`x^(4)+y^(4)+x^(2)y^(2)=c`

B

`x^(4)+y^(4)+3x^(2)y^(2)=c`

C

`x^(4)+y^(4)+6x^(2)y^(2)=c`

D

`x^(4)+y^(4)+9x^(2)y^(2)=c`

Text Solution

Verified by Experts

The correct Answer is:
C
put `y=vx`
Differential equal becomes
`int(4(v^(3)+3v))/(v^(4)+6v^(2)+1)dv=-4int(dx)/(x)`
`ln(v^(4)+6v^(2)+1)=-4lnx+lnc`
`impliesx^(4)+y^(4)+6x^(2)y^(2)=c`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE|Exercise PART : 1MATHEMATICS SEC - 1|1 Videos

  • TEST PAPERS

    RESONANCE|Exercise PART : 1MATHEMATICS|9 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

  • TEST SERIES

    RESONANCE|Exercise MATHEMATICS|131 Videos

Similar Questions

Explore conceptually related problems

Solution of the differential equation (dy)/(dx)=x^(2)y+y is

The solution of the differential equation x(dy)/(dx)+y = y^2 is

The solution of the differential equation x+y(dy)/(dx)=2y is

The solution of the differential equation (dy)/(dx)=(3x^(2)y^(4)+2xy)/(x^(2)-2x^(3)y^(3)) is

If y(4)=-2 ,then the solution of differential equation (dy)/(dx)=(y(x+y^(3)))/(x(y^(3)-x)) is

The solution of the differential equation (dy)/(dx) = e^(3x-2y) +x^(2)e^(-2y) ,is

Solution of the differential equation y dx+(x-y^(2))dy=0 is

Solution of the differential equation (dy)/(dx)=(4x-3y)/(3x-2y) is

Solution of the differential equation (dy)/(dx)+(x-2y)/(2x-y)=0 is

The solution of the differential equation x^(3)(dy)/(dx)=y^(3)+y^(2)sqrt(y^(2)-x^(2)) is :

RESONANCE-TEST PAPERS-MATHEMATICS
  1. the solution of the differential equation (dy)/(dx)+(x(x^(2)+3y^(2))/(...

    Text Solution

    |

  2. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  3. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

    Text Solution

    |

  4. If f(x)=x+tanx and g(x) is inverse of f(x) then g^(')(x) is equal to

    Text Solution

    |

  5. Tangents PA and PB are drawn to parabola y^(2)=4x from any arbitrary p...

    Text Solution

    |

  6. If lim(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" ...

    Text Solution

    |

  7. Eccentricity of ellipse 2(x-y+1)^(2)+3(x+y+2)^(2)=5 is

    Text Solution

    |

  8. If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y. Then which ...

    Text Solution

    |

  9. If f:RrarrR is a continuous function satisfying f(0)=1 and f(2x)-f(x)=...

    Text Solution

    |

  10. tan^(-1)(sinx)=sin^(-1)(tanx) holds true for

    Text Solution

    |

  11. is The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not ...

    Text Solution

    |

  12. Consider parabola P(1)-=y=x^(2) and P(2)-=y^(2)=-8x and the line L-=lx...

    Text Solution

    |

  13. If the normals at (x(i),y(i)) i=1,2,3,4 to the rectangular hyperbola x...

    Text Solution

    |

  14. Let f(x)=x^(3)-x^(2)+x+1 and g(x)={("max "f(t) 0letlex 0lexle1),(3-x 1...

    Text Solution

    |

  15. The value(s) of x satisfying tan^(-1)(x+3)-tan^(-1)(x-3)=sin^(-1)(3/5)...

    Text Solution

    |

  16. For an ellipse having major and minor axis along x and y axes respecti...

    Text Solution

    |

  17. If f:[0,1]rarrR is defined as f(x)={(x^(3)(1-x)"sin"1/(x^(2)) 0ltxle1)...

    Text Solution

    |

  18. If f(x)=root (3)(8x^(3)+mx^(2))-nx such that lim(xrarroo)f(x)=1 then

    Text Solution

    |

  19. For the curve y=4x^3-2x^5,find all the points at which the tangent pa...

    Text Solution

    |

  20. Minimum value of (sin^(-1)x)^(2)+(cos^(-1)x)^(2) is greater than

    Text Solution

    |

  21. If y+a=m(1)(x+3a),y+a=m(2)(x+3a) are two tangents to the parabola y^(2...

    Text Solution

    |