# Solve in series the equation d2y/dx2+x2y= 0 .

1
by TustiJaggi

## Answers

2015-09-14T17:08:53+05:30

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See also:  http://brainly.in/question/183933.  which I have solved.

This differential equations is called Fowler's second order differential (non-linear) equation.  The solution is not found in closed expression of known simple functions.  We can find the answer by using Taylor series expansion for y(x).

Solving    d²y/dx² = - x² y    --- (1)

When we differentiate y(x) wrt x twice, the exponent of x reduces by 2 in y".  On the RHS of (1) we have x² y, so exponent is increased by 2.  Equation (1) will be valid if the exponent of x of  (n+1)th term = 4 + exponent of n th term.

We can find two linearly independent solutions as:

Similarly for another independent solution :

Now we have the final general solution as :

here c1 and c2 are real constants.

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have you typed it??
yes of course. I typed it all -- it took nearly an hour to complete it and to check it... i answered the same earlier in another question -- i mentioned that in the answer... that took also more than one hour