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    convert y''(x)-(x+0.5)y'(x)-(x+3.2)y(x)=0.8x+1.3 into first order differential equation. Same for y'''(x)-3y'(x)-xy=0
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    (Original post by studentdadada)
    convert y''(x)-(x+0.5)y'(x)-(x+3.2)y(x)=0.8x+1.3 into first order differential equation. Same for y'''(x)-3y'(x)-xy=0
    Assuming that an analytic solution exists you need to find a substitution first to get rid of the variable coefficients.

    A good book on ODEs will give some clues as to how to do this, for certain type of ODEs.

    Things like y=xv(x) and y=exv(x) are common substitutions, but I fear they will not work here because both the coefficients of y' and y are linear in x.

    (from another post of yours which enquires about numerical techniques are you looking for solutions in terms of standard common functions?)
 
 
 

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