Home
Class 12
MATHS
Solution of the differential y' = (3yx^(...

Solution of the differential y' = `(3yx^(2))/(x^(3)+2y^(4))` is

A

`x^(3)y^(-1)=(2)/(3)y^(3)+c`

B

`x^(2)y^(-1)=(2)/(3)y^(3)+c`

C

`xy^(-1)=(2)/(3)y^(3)+c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(3yx^(2))dx - x^(3)dy = 2y^(4)dy`
`rArr" "yd(x^(3))-x^(3)dy = 2y^(4)dy`
`rArr" "(yd(x^(3))-x^(3)dy)/(y^(2))=2y^(2)dy`
`rArr" "d((x^(3))/(y))=2y^(2)dy`
`rArr" "(x^(3))/(y)=(2)/(3)y^(3)+c`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Verify that the function y = e^(-3x) is a solution of the differential equation (d^(2)y)/(dx^(2)) + (dy)/(dx) - 6y = 0

Show that the function y= A cos 2x - B sin 2x is a solution of the differential equation (d^(2)y)/(dx^(2)) + 4y = 0

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

The solution of the differential equation (y^(2)+2x)(dy)/(dx)=y satisfies x=1, y=1 . Then the solution is

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

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

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

The solution of the differential equation x=1+x y(dy)/(dx)+(x^2y^2)/(2!)((dy)/dx)^2+(x^3y^3)/(3!)((dy)/(dx))^3+... i s

A solution of the differential equation (x^(2) y^(2) - 1) dy + 2xy ^(3) dx = 0 is-

Number of values of m in N for which y=e^(m x) is a solution of the differential equation (d^3y)/(dx^3)-3(d^2y)/(dx^2)-4(dy)/(dx)+12 y=0 (a) 0 (b) 1 (c) 2 (d) More than 2

CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. Solution of the differential (x+2y^(3))=(dx)/(dy)y is

    Text Solution

    |

  2. General solution of differential equation x^(2)(x+y(dy)/(dx))+(x(dy)/(...

    Text Solution

    |

  3. Solution of the differential y' = (3yx^(2))/(x^(3)+2y^(4)) is

    Text Solution

    |

  4. For y gt 0 and x in R, ydx + y^(2)dy = xdy where y = f(x). If f(1)=1, ...

    Text Solution

    |

  5. An equation of the curve satisfying x dy - y dx = sqrt(x^(2)-y^(2))dx ...

    Text Solution

    |

  6. The solution of (y(1+x^(-1))+siny)dx +(x+log x +x cos y)dy=0 is

    Text Solution

    |

  7. The solution of (1+x)(dy)/(dx)+1=e^(x-y) is

    Text Solution

    |

  8. The solution of differential equation x sec((y)/(x))(y dx + x dy)="y c...

    Text Solution

    |

  9. Solvex dy + y dx = (ydx - xdy)/(x^2 + y^2)

    Text Solution

    |

  10. (1 + xy) ydx + (1-xy)xdy = 0

    Text Solution

    |

  11. Solution of the differential equation dy/dx=(y^3)/(e^(2x)+y^2) , is

    Text Solution

    |

  12. A popular grows at the rate of 10% of the population per year. How lon...

    Text Solution

    |

  13. A tangent drawn to the curve y = f(x) at P(x, y) cuts the x and y axes...

    Text Solution

    |

  14. A curve 'C' with negative slope through the point(0,1) lies in the I Q...

    Text Solution

    |

  15. Tangent to a curve intercepts the y-axis at a point Pdot A line ...

    Text Solution

    |

  16. The orthogonal trajectories of the family of curves an a^(n-1)y = x^n ...

    Text Solution

    |

  17. Suppose a curve whose sub tangent is n times the abscissa of the point...

    Text Solution

    |

  18. Let C be a curve such that the normal at any point P on it meets x-axi...

    Text Solution

    |

  19. The normal at a general point (a, b) on curve makes an angle theta wit...

    Text Solution

    |

  20. Tangent is drawn at the point (xi ,yi) on the curve y=f(x), which ...

    Text Solution

    |