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Math Help - linear ordinary differential equations

  1. #1
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    linear ordinary differential equations

    Hi everyone

    Need help to verify this workings, thank you in advance for qall your help & support.

    Solve the following linear ordinary differential equations

    i) \frac{dy}{dx} -y=2
    \int\frac{dy}{y+2}=\int dx+c'
    y+2=ce^x

    ii) \frac{dy}{dx} + 5y=e^{-2x}
    Integral factor
    e^{\int5dx}=e^{5x}

    Multiply by U.F & integrate
    e^{5x}.y=\int e^{5x}.e^{-2x}dx + c]
    ye^{5x}=\frac{1}{3}e^{3x}+c or
    y = \frac{1}{3}e^{-2x}+ce^{-5x}
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  2. #2
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    That is correct. You can check it by observing that y'=ce^x so y'-y = ce^x - (ce^x - 2) = 2.
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  3. #3
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by anderson View Post
    Hi everyone

    Need help to verify this workings, thank you in advance for qall your help & support.

    Solve the following linear ordinary differential equations

    i) \frac{dy}{dx} -y=2
    \int\frac{dy}{y+2}=\int dx+c'
    y+2=ce^x
    That is correct. Just FYI that particular DE is known as a seperable differential equation.
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