Home
Class 12
MATHS
Solve the differential equation y e^(x/y...

Solve the differential equation `y e^(x/y)dx=(x e^(x/y)+y^2)dy(y!=0)`

Text Solution

Verified by Experts

We have `ye^(x/y)dx-xe^(x/y)dy=y^(2)dy`
`therefore e^(x/y)(ydx-xdy)/(y^(2))=dy`
`rArr inte^(x/y)d(x/y)=intdy`
`rArr e^(x/y)=y+c`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.1|6 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.2|6 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

Solve the differential equation (x+y)dy=(x-y)dx

Solve the differential equation ye^((x)/(y))dx=(xe^((x)/(y))+y^(2))dy(y!=0)

Solve the differential equation (dy)/(dx)+y = e^(-x)

Solve the differential equation (dy)/(dx)=x^2y+y

Solve the differential equation dy/dx + 1 = e^(x+y)

Solve the differential equation (dy)/(dx)+1=e^(x+y)

Show that the differential equation 2y e^(x/y)dx+(y-2x e^(x/y))dy=0 is homogeneous and find its particular solution, given that, x" "=" "0 wheny" "=" "1 .

Solve the differential equations: (x-y)dy+(x+y)dx=0

solve the differential equation (y+x)(dy)/(dx)=y-x

solve the differential equation (dy)/(dx)=e^(x+y)+x^(2)e^(y)

CENGAGE-DIFFERENTIAL EQUATIONS-Question Bank
  1. Solve the differential equation y e^(x/y)dx=(x e^(x/y)+y^2)dy(y!=0)

    Text Solution

    |

  2. A function is continuous and differentiable on R0 satisfying x f^(prim...

    Text Solution

    |

  3. A curve y=f(x) is passing through (0,0). If the slope-of the curve at ...

    Text Solution

    |

  4. If y=f(x) satisfies the differential equation (1+x^2) f^(prime)(x)=x(1...

    Text Solution

    |

  5. If y(x) is solution of (x+1) (d y)/(d x)-x y=1, y(0)=-1, then y(-6/5) ...

    Text Solution

    |

  6. Let perpendicular distance of any variable tangent on the curve C fro...

    Text Solution

    |

  7. The number of straight lines which satisfies the differential equation...

    Text Solution

    |

  8. The real valuc of m for which the 'substitution, y=u^m will transform ...

    Text Solution

    |

  9. A function y=f(x) satisfies the differential equation (d y)/(d x)+x^2 ...

    Text Solution

    |

  10. If the differential equation representing the family of curves y=C1 co...

    Text Solution

    |

  11. The family of integral curves of the differential equation (d y)/(d x)...

    Text Solution

    |

  12. If ' e' denotes tho cccentricity of the hyperbola, satisfying the dif...

    Text Solution

    |

  13. A carve y=f(x) passes through O(0,0) and slope of tangent line at any ...

    Text Solution

    |

  14. If y=x sin (ln x) is the solution of x^2((d y)/(d x))^2-(lambda-2) x ...

    Text Solution

    |

  15. Let y=f(x) be drawn with f(0)=2 and for each real number ' a ' the lin...

    Text Solution

    |

  16. If tangent to the curve x y=x^2+1 at (alpha, beta) is normal to the cu...

    Text Solution

    |

  17. If y=y(x) and it follows the relation 4 x e^v=y+5 sin ^2 x then y^prim...

    Text Solution

    |

  18. Given y(0)=2000 and (d y)/(d x)=32000-20 y^2, then find the value of u...

    Text Solution

    |

  19. If the differential equation corresponding to the family of curves, y=...

    Text Solution

    |

  20. A curve in the first quadrant is such that the area of the triangle fo...

    Text Solution

    |

  21. Number of values of m in N for which y=e^(mx) is a solution of the di...

    Text Solution

    |