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Math Help - Solving differential equations by inspection!

  1. #1
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    Solving differential equations by inspection!

    I have this question 1. Solve the following DEs, by inspection.
    y= -sin x

    I Know that y=cos x and y'= -sin x. Then is y=cos x the answer? What does it mean when solve by inspection???
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  2. #2
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    Re: Solving differential equations by inspection!

    Solving by inspection involves exactly what you did (well, almost, you forgot the constant of integration)...you know that:

    \frac{dy}{dx}=\frac{d}{dx}(\cos(x)+C)=-\sin(x) and so we must have:

    y=\cos(x)+C
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  3. #3
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    Re: Solving differential equations by inspection!

    Oh thanks for the reply!

    Then let's say for y'' = 3 and I did. y'=3x+c
    y= (3/2)x^2 +C

    Then is y= (3/2)x^2 + C answer for y"=3?

    Thank you.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Solving differential equations by inspection!

    No, for the second example, you should observe that:

    \frac{d^2}{dx^2}\left(\frac{3}{2}x^2+c_1x+c_2 \right)=3 hence:

    y=\frac{3}{2}x^2+c_1x+c_2
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