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# how to solve 4th order differential equations

Posted 9 years ago
 Hi could you please help me out to solve a 4th order differential equation in mathematica with initial values: Regards
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Posted 9 years ago
 Thank You S M Blinder its a gr8 help Regards
Posted 9 years ago
 A first step might be to solve the homogeneous equation:In:= DSolve[D[y[x], {x, 4}] - x y[x] == 0, y[x], x] Out= {{y[x] -> C HypergeometricPFQ[{}, {2/5, 3/5, 4/5}, x^5/625] + (1/(5^( 4/5)))(-1)^(1/5) x C HypergeometricPFQ[{}, {3/5, 4/5, 6/5}, x^5/625] + (1/( 5 5^(3/5)))(-1)^(2/5) x^2 C HypergeometricPFQ[{}, {4/5, 6/5, 7/5}, x^5/625] + (1/( 25 5^(2/5)))(-1)^(3/5) x^3 C HypergeometricPFQ[{}, {6/5, 7/5, 8/5}, x^5/625]}} then try one of the standard techniques for the corresponding inhomogeneous equation.For a numerical solution In:= NDSolve[{D[y[x], {x, 4}] - x y[x] == -(11 + 9 x + x^2 - x^3) E^x, y[-1] == 0, y == 0, y'[-1] == 2/E, y' == -2/E}, y[x], x] Out= {{y[x] -> \!$$\* TagBox[ RowBox[{"InterpolatingFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"-", "1."}], ",", "1."}], "}"}], "}"}], ",", "\<\"<>\"\>"}], "]"}], False, Editable->False]$$[x]}} 
Posted 9 years ago
 Look at the examples in the documentation for NDSolveNDSolvetry to carefully model your input after the examples, and use E for Euler's constant, or use one of the palettes to enter a desktop-published version of E. Watch carefully that it is always y''''[t] and y[t], not the more usual math notation of y''''' and y.See if that provides you with enough insight to complete this.