I am solving the following equation using Dsolve command in Mathematica:
DSolve[a1*y''[x] + y''''[x] == 0, y[x], x]
The general solution of these equations are of the form:
y = c1+c2*x+c3*Cos[Sqrt[a1]*x]+c4*Sin[Sqrt[a1]*x]
But, Mathematica gives me the following solution:
C + x C + (-((C Cos[x Sqrt[a1]])) - (C Sin[x Sqrt[a1]]))/a1
Although, both of the solutions are equivalent since you can always you can change your constants, however, I want the general solution (
y= c1+c2*x+c3*Cos[Sqrt[a1]*x]+c4*Sin[Sqrt[a1]*x]) as the output from Mathematica. Can you please suggest what additional conditions I need to impose so that Mathematica gives result exactly as general solution?
Thank you very much for your help!