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Hi, I was solving the following second order ODE:

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21x%5E2%20y%5E%27%27-5xy%5E%27%2B5y%3Dx%5E6%20sinx.gif [Broken]

I used variation of parameters and found this solution:

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21y%3DC_1%20x%20%2B%20C_2%20x%5E5%20-%20180%20x%20Cosx%20%2B%2090%20x%5E3%20Cosx%20-%20%20%207%20x%5E5%20Cosx%20-%20180%20x%5E2%20Sinx%20%2B%2030%20x%5E4%20Sinx%20-%20x%5E6%20Sinx.gif [Broken]

However if I try DSolve in mathematica, the answer I get is instead:

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21y%5Bx%5D%20-%3E%20x%20C%5B1%5D%20%2B%20x%5E5%20C%5B2%5D%20%2B%206%20x%20Cos%5Bx%5D%20-%203%20x%5E3%20Cos%5Bx%5D%20%2B%206%20x%5E2%20Sin%5Bx%5D%20-%20%20%20x%5E4%20Sin%5Bx%5D.gif [Broken]

Can anyone verify my answer? (Warning: quite long to integrate) Either I'm typing something wrong in mathematica, I miscalculated the solution or mathematica uses the wrong algorithm.

Thanks.

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21x%5E2%20y%5E%27%27-5xy%5E%27%2B5y%3Dx%5E6%20sinx.gif [Broken]

I used variation of parameters and found this solution:

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21y%3DC_1%20x%20%2B%20C_2%20x%5E5%20-%20180%20x%20Cosx%20%2B%2090%20x%5E3%20Cosx%20-%20%20%207%20x%5E5%20Cosx%20-%20180%20x%5E2%20Sinx%20%2B%2030%20x%5E4%20Sinx%20-%20x%5E6%20Sinx.gif [Broken]

However if I try DSolve in mathematica, the answer I get is instead:

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21y%5Bx%5D%20-%3E%20x%20C%5B1%5D%20%2B%20x%5E5%20C%5B2%5D%20%2B%206%20x%20Cos%5Bx%5D%20-%203%20x%5E3%20Cos%5Bx%5D%20%2B%206%20x%5E2%20Sin%5Bx%5D%20-%20%20%20x%5E4%20Sin%5Bx%5D.gif [Broken]

Can anyone verify my answer? (Warning: quite long to integrate) Either I'm typing something wrong in mathematica, I miscalculated the solution or mathematica uses the wrong algorithm.

Thanks.

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