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  1. #1
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    solving differential equations help

    I need help in solving differential equations

    Code:
    1- xy' - y = x^2
    
    2- y' -y/x = x sinx
     
    3- y' -3x^2 y = (4 x e ^(x^3))/sqrt(1+(x^2))
    
    4- y'-y/x = x cos x

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  2. #2
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    Re: solving differential equations help

    they are all first order linear ordinary differential equations
    there are a variety of methods used, which may be found on the internet

    you can check the answers with wolfram alpha:
    go to the wolfram alpha website and type something like find y for xy' - y = x^2
    enter and wait. it will give you the solution but won't tell you how to do it.



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  3. #3
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    _Eduardo_'s Avatar
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    Re: solving differential equations help

    Quote Originally Posted by joniengr View Post
    I need help in solving differential equations

    Code:
    1- xy' - y = x^2
    
    2- y' -y/x = x sinx
     
    3- y' -3x^2 y = (4 x e ^(x^3))/sqrt(1+(x^2))
    
    4- y'-y/x = x cos x

    Hint:
    Code:
    xy' - y = x^2 (y/x)'
    and
    Code:
    y' -3x^2 y = (y e^(-x^3))' e^(x^3)


    Then
    Code:
    1- x^2 (y/x)' = x^2  -----> solve  (y/x)' = 1
    
    2- x (y/x)' = x sinx   -----> solve  (y/x)' = sinx
    
    3- (y e^(-x^3))' e^(x^3) = (4 x e ^(x^3))/sqrt(1+(x^2)) -----> solve  (y e^(-x^3))' = (4 x)/sqrt(1+(x^2))
     
    4- x (y/x)' = x cosx  -----> solve  (y/x)' = cosx
    All are easy to integrate.



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