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# Differential Equations solver issues

Posted 10 years ago
 Hello I have been having trouble with the differential equations solving applications. For instance on the D.E. 4y''-4y' +y = e^(x/2)sqrt(1-x^2), The step by step solution seems to have it correct until it simplifies Yp(X). http://www.wolframalpha.com/input/?i=4y%27%27-4y%27%2By+%3D+e%5E%28x%2F2%29sqrt%281-x%5E2%29 Here is the link to the equation. How does YpX simplify that dramatically? I even typed the simplified equation in question right into the wolfram alpha engine and it simplified it differently. (It simplified it exactly the way i did it by hand) Therefore is there a step missing in the step by step solution? Or is there something wrong with the algorithm? I will humbly accept any mathematical criticism for being wrong. I am not saying that Wolfram Alpha is wrong, (most likely myself) however It would be nice if someone would look at it.
 Are you referring to "The particular solution is thus: " to "Simplify"? The solution is correct by factoring out $1/24 \times e^{x/2}$ then you just combine the terms with the same exponential or radical factors: I guess you may have overlooked the simplified form of Sqrt[1-x^2]^(3/2).