Home
Class 12
MATHS
Find the equation of the curve passing ...

Find the equation of the curve passing through the point (1, 1) whose differential equation is `x dy =(2x^2+1)dx(x!=0)`.

Text Solution

AI Generated Solution

To find the equation of the curve passing through the point (1, 1) whose differential equation is given by \( x \, dy = (2x^2 + 1) \, dx \), we will follow these steps: ### Step 1: Rewrite the differential equation We start with the given equation: \[ x \, dy = (2x^2 + 1) \, dx \] Dividing both sides by \( x \) (assuming \( x \neq 0 \)): ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.3|12 Videos
  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.5|17 Videos
  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.4|23 Videos
  • DETERMINANTS

    NCERT ENGLISH|Exercise All Questions|116 Videos
  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.4|25 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the curve passing through the point (1,1) whose differential equation is : xdy=(2x^2+1)dx

Find the equation of the curve passing through the point (1,1) whose differential equation is : xdy=(2x^2+1)dxdot

Find the equation of the curve passing through the point (1, -1) whose differential equation is xy(dy)/(dx)=(x+2)(y+2)

Find the equation of a curve passing through the point (0, 0) and whose differential equation is y^(prime)=e^ xsinx

Find the equation of a curve passing through the point (0, 0) and whose differential equation is y^(prime)=e xsinx

Find the equation of the curve passing through the point (0,pi/4) whose differential equation is sinx cosy dx + cosx siny dy = 0 .

Find the equation of the curve passing through origin and satisfying the differential equation 2xdy = (2x^(2) + x) dx .

Show that the equation of the curve passing through the point (1,0) and satisfying the differential equation (1+y^2)dx-xydy=0 is x^2-y^2=1

The equation of the curve passing through the point (1,1) and satisfying the differential equation (dy)/(dx) = (x+2y-3)/(y-2x+1) is

The equation of the curve passing through the origin and satisfying the differential equation ((dy)/(dx))^(2)=(x-y)^(2) , is

NCERT ENGLISH-DIFFERENTIAL EQUATIONS-SOLVED EXAMPLES
  1. Show that the differential equation xcos(y/x)(dy)/(dx)=ycos(y/x)+x ...

    Text Solution

    |

  2. Find the equation of a curve passing through the point (2, 3), given ...

    Text Solution

    |

  3. Find the equation of the curve passing through the point (1, 1) whose...

    Text Solution

    |

  4. Find the general solution of the differential equation (dy)/(dx)-y=co...

    Text Solution

    |

  5. Show that the family of curves for which the slope of the tangent at ...

    Text Solution

    |

  6. Form the differential equation representing the family of ellipses ha...

    Text Solution

    |

  7. Form the differential equation of the family of circles touching the ...

    Text Solution

    |

  8. Form the differential equation representing the family of curves y = ...

    Text Solution

    |

  9. Find the differential equation representing the family of curves y=asi...

    Text Solution

    |

  10. Verify that the function y=e^(-3x)is a solution of the differential eq...

    Text Solution

    |

  11. Verify that the functiony = a cos x + b sin x, where, a, b in Ris a ...

    Text Solution

    |

  12. Find the order and degree, if defined, of each of the following differ...

    Text Solution

    |

  13. Form the differential equation representing the family of parabolas h...

    Text Solution

    |

  14. Find the general solution of the differential equation (dy)/(dx)=(x+1...

    Text Solution

    |

  15. Solve the differential equation (tan^(-1)y-x)dy=(1+y^2)dx.

    Text Solution

    |

  16. Verify that the function y=c1e^(ax ) """"cosb x+c2""""e^(ax)"" si...

    Text Solution

    |

  17. Form the differential equation of the family of circles in the second...

    Text Solution

    |

  18. Find the particular solution of the differential equation log ((dy)/(d...

    Text Solution

    |

  19. Solve the differential equation (x dy-y dx)ysin(y/x)=(y dx+x dy)xcos(...

    Text Solution

    |

  20. Find the general solution of the differential equation x(dy)/(dx)+2y=...

    Text Solution

    |