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# How to solve this differential equation?

Posted 10 years ago
 Hi all, I want to solve the following differential equation but seems like mathematica does not have any answer. Anyone's help is appreciated. DSolve[y''[x] == y[x]/(x^2 + a^2)^1.5, y[x], x]  And Mathematica returns me nothing. Sincerely, Suvadip Attachments:
 As the manual says Apply N[DSolve[...]] to invoke NDSolve if symbolic solution fails: In[13]:= With[{a = 2}, DSolve[{y''[x] == y[x]/(x^2 + a^2)^(3/2), y'[0] == 1, y[0] == 2}, y, {x, 0, 4}] ] Out[13]= DSolve[{(y^\[Prime]\[Prime])[x] == y[x]/(4 + x^2)^(3/2), Derivative[1][y][0] == 1, y[0] == 2}, y, {x, 0, 4}] In[14]:= N[%] Out[14]= {{y -> InterpolatingFunction[{{0., 4.}}, <>]}} Numerical solution urges you to define boundary conditions and an evaluation interval for the independent variable x. For some integer exponents DSolve[y''[x] == y[x]/(x^2 + a^2), y, x] DSolve[y''[x] == y[x]/(x^2 + a^2)^2, y, x] DSolve does not return the input.