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Thread: differential equation of y''+y'-6y =0 is my answer correct

  1. #1
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    differential equation of y''+y'-6y =0 is my answer correct

    find the general solution of the differential equation y''+y'-6y =0
    y''+y'-6y

    m + m - 6 = 0
    m-2(m+3)=0
    m-2=0m-3=0
    m-2=0m+3=0

    yᶜ = C₁℮^(-3x) + C₂℮^(2x)

    find the particular solution of
    y''+y'-6y =0 given that y(0)= 5 and y'(0)=0 getting trouble with this part help please
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  2. #2
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    Re: differential equation of y''+y'-6y =0 is my answer correct

    Quote Originally Posted by JadaPsherman View Post
    find the general solution of the differential equation y''+y'-6y =0
    y''+y'-6y

    m + m - 6 = 0
    m-2(m+3)=0
    m-2=0m-3=0
    m-2=0m+3=0

    yᶜ = C₁℮^(-3x) + C₂℮^(2x)

    find the particular solution of
    y''+y'-6y =0 given that y(0)= 5 and y'(0)=0 getting trouble with this part help please
    $y(x) = C_1 e^{-3x}+C_2 e^{2x}$

    $y^\prime(x)= -3C_1 e^{-3x} + 2 C_2 e^{2x}$

    $y(0) = 5 = C_1+C_2$

    $y^\prime(0) = 0 = -3C_1 + 2 C_2$

    $C_2 = \dfrac 3 2 C_1$

    $\dfrac 5 2 C_1 = 5$

    $C_1 = 2, C_2 = 3$

    $y(x) = 2 e^{-3x} + 3 e^{2x}$
    Thanks from JadaPsherman
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  3. #3
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    Re: differential equation of y''+y'-6y =0 is my answer correct

    oh wow i had i right all along i had the 3/2 5/2 . thanks alot
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  4. #4
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    Re: differential equation of y''+y'-6y =0 is my answer correct

    Hello, JadaPsherman!

    Find the general solution of: .$\displaystyle y'' +y'-6y \:=\:0$

    $\displaystyle m^2 + m - 6 \:=\: 0 \quad\Rightarrow\quad (m-2)(m+3)\:=\:0 \quad\Rightarrow\quad m \:=\:2,-3$

    $\displaystyle y \:=\: C_{_1} e^{2x} + C_{_2} e^{-3x}$

    This is correct!




    Find the particular solution of $\displaystyle y''+y'-6y \:=\:0$
    given that $\displaystyle y(0)= 5$ and $\displaystyle y'(0)=0$

    You have: .$\displaystyle y(x) \;=\;C_{_1}e^{2x} + C_{_2}e^{-3x}$

    We are told that $\displaystyle y(0) = 5.$

    . . $\displaystyle C_{_1}e^0 + C_{_2}e^0 \:=\:5 \quad\Rightarrow\quad \bf{\color{red}C_1 + C_2 \:=\:5}$


    We have: .$\displaystyle y'(x) \:=\:2C_{_1}e^{2x} -3C_{_2}e^{-3x}$

    We are told that $\displaystyle y'(0) = 0.$

    . . $\displaystyle 2C_{_1}e^0 -3C_{_2}e^0 \:=\:0 \quad\Rightarrow\quad \bf{\color{red}2C_1 - 3C_2 \:=\:0}$


    Solve the system of equations: .$\displaystyle C_1 = 3,\;C_2 = 2$

    Therefore: .$\displaystyle y \;=\;3e^{2x} + 2e^{-3x}$


    Um ... too slow!
    .
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  5. #5
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    Re: differential equation of y''+y'-6y =0 is my answer correct

    Quote Originally Posted by JadaPsherman View Post
    find the general solution of the differential equation y''+y'-6y =0
    y''+y'-6y

    m + m - 6 = 0
    m-2(m+3)=0

    You need to be more careful how you write things. (m- 2)(m+ 3)= m+ m- 6 but m-2(m+ 3)= m- 2m- 6= -m- 6.

    m-2=0m-3=0
    m-2=0m+3=0
    And here you need spaces to make it clear that these are two separate equations:
    m- 2= 0 and m+ 3= 0 (NOT "m- 3= 0"!)

    yᶜ = C₁℮^(-3x) + C₂℮^(2x)

    find the particular solution of
    y''+y'-6y =0 given that y(0)= 5 and y'(0)=0 getting trouble with this part help please
    Follow Math Help Forum on Facebook and Google+

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