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Thread: (d2x/dt2) +4(dx/dt) +3x= e^-3x

  1. #1
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    (d2x/dt2) +4(dx/dt) +3x= e^-3x

    is the given answer wrong ?
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  2. #2
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    Re: (d2x/dt2) +4(dx/dt) +3x= e^-3x

    (d2x/dt2) +4(dx/dt) +3x= e^-3x-capture.png
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  3. #3
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    Re: (d2x/dt2) +4(dx/dt) +3x= e^-3x

    Quote Originally Posted by xl5899 View Post
    Click image for larger version. 

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  4. #4
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    Re: (d2x/dt2) +4(dx/dt) +3x= e^-3x

    It's not that difficult to type the problem in rather than asking people you want to help you to open and image!

    The problem you have is to show that x(t)= (1/2)(1- t)e^(-3t) satisfies the differential equation d^2 x/d^2+ 4dy/dx+ 3x= e^(-3t) with initial conditions x(0)= 1/2, x'(0)= -2.

    First x(0)= (1/2)(1- 0)e^0= (1/2)(1)(1) so that the first condition, x(0)= 1/2, is satisfies.

    Second, x'(t)= (1/2)(-1)e^(-3t)- (3/2)(1- t)e^(-3t)= (-2+ (3/2)t)e^(-3t) so x'(0)=(-2+ 0)e^0= -2 so the second condition, x'(0)= -2, is satisfied.

    Finally, x''(t)= (3/2)e^(-3t)- (3)(-2+ (3/2)t)e^(-3t)= (15/2- (9/2)t)e^(3t) so that

    x''+ 4x'+ 3x= (15/2- (9/2)t)e^(3t)+ 4(-2+ (3/2)t)e(-3t))+ 3(1/2)(1- t)e^(-3t)= [(15/2- 9+ 3/2)- (9/2+ 6- 3/2)t] e^(-3t)= -9 t e^(-3t) NOT e^(-3t).
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    Re: (d2x/dt2) +4(dx/dt) +3x= e^-3x

    Quote Originally Posted by HallsofIvy View Post
    It's not that difficult to type the problem in rather than asking people you want to help you to open and image!

    The problem you have is to show that x(t)= (1/2)(1- t)e^(-3t) satisfies the differential equation d^2 x/d^2+ 4dy/dx+ 3x= e^(-3t) with initial conditions x(0)= 1/2, x'(0)= -2.

    First x(0)= (1/2)(1- 0)e^0= (1/2)(1)(1) so that the first condition, x(0)= 1/2, is satisfies.

    Second, x'(t)= (1/2)(-1)e^(-3t)- (3/2)(1- t)e^(-3t)= (-2+ (3/2)t)e^(-3t) so x'(0)=(-2+ 0)e^0= -2 so the second condition, x'(0)= -2, is satisfied.

    Finally, x''(t)= (3/2)e^(-3t)- (3)(-2+ (3/2)t)e^(-3t)= (15/2- (9/2)t)e^(3t) so that

    x''+ 4x'+ 3x= (15/2- (9/2)t)e^(3t)+ 4(-2+ (3/2)t)e(-3t))+ 3(1/2)(1- t)e^(-3t)= [(15/2- 9+ 3/2)- (9/2+ 6- 3/2)t] e^(-3t)= -9 t e^(-3t) NOT e^(-3t).
    if i wanna follow the original question , is my answer correct ?
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    Re: (d2x/dt2) +4(dx/dt) +3x= e^-3x

    i found the answer already , thanks for the help
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