Home
Class 12
MATHS
Solve the following differential equatio...

Solve the following differential equation: `(dy)/(dx)+y=sinx`

Text Solution

Verified by Experts

Given differential equation is `frac{d y}{d x}+y=sin x`

`I F=int e^{1 d x}=e^{x}`

The general solution is

`` `y {e}^{{x}}=int {e}^{{x}} sin {xdx}+{C}` ……………{ (i) }

`` Let `int e^{x} sin x d x`

`` ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos
  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

Similar Questions

Explore conceptually related problems

Solve the following differential equation: (dy)/(dx)+y=4x

Solve the following differential equations (dy)/(dx)=x

Solve the following differential equation: (dy)/(dx)+2y=4x

Solve the following differential equation: (dy)/(dx)+y=cos x

Solve the following differential equations (dy)/(dx)=sinx*siny

Solve the following differential equation: x(dy)/(dx)-y=x^2

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

Solve the following differential equations: x(dy)/(dx)=x+y

Solve the following differential equations (dy)/(dx)=cotx

Solve the following differential equation: (dy)/(dx)+y=e^(-2x)

RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve the following differential equation: (dy)/(dx)+2y=4x

    Text Solution

    |

  2. Solve the following differential equations: x(dy)/(dx)-y=(x-1)e^x

    Text Solution

    |

  3. Solve the following differential equation: (dy)/(dx)+y=sinx

    Text Solution

    |

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

    Text Solution

    |

  5. The solution of differential equation (1+x^(2)) (dy)/(dx) + y = e^(...

    Text Solution

    |

  6. Solve the differential equation: (i) (1+y^2) + ( x - e^(tan^-1 y) ) d...

    Text Solution

    |

  7. Solve the following differential equation: dx+x dy=e^(-y)sec^2y\ dy

    Text Solution

    |

  8. Solve differential equation: (x^2-1)(dy)/(dx)+2(x+2)y=2\ (x+1)

    Text Solution

    |

  9. Solve differential equation (x+2y^2)(dy)/(dx)=y , given that when x=2,...

    Text Solution

    |

  10. Find one parameter families of solution curves of the following differ...

    Text Solution

    |

  11. Find one parameter families of solution curves of the following differ...

    Text Solution

    |

  12. Find one parameter families of solution curves of the following differ...

    Text Solution

    |

  13. Find one parameter families of solution curves of the differential equ...

    Text Solution

    |

  14. Find one parameter families of solution curves of the following differ...

    Text Solution

    |

  15. Solve each of the following initial value problem: y^(prime)+y=e^x ,\ ...

    Text Solution

    |

  16. Solve each of the following initial value problem: x(dy)/(dx)-y=logx ,...

    Text Solution

    |

  17. Solve the following initial value problem: (dy)/(dx)+2y=e^(-2x)sinx ,\...

    Text Solution

    |

  18. Solve the following initial value problem: (1+y^2)dx+(x-e^(-tan^(-1)y)...

    Text Solution

    |

  19. Solve each of the following initial value problem: (dy)/(dx)+\ y\ t a ...

    Text Solution

    |

  20. Solve the following initial value problem: (dy)/(dx)+ycotx=2cosx ,\ y\...

    Text Solution

    |