Question

Second order differential equations:
100(y'')-20(y)+y=0. Find general solution.
Please explain how to obtain the general solution.

Answer 1

PLEASE EXPLAIN STEPWISE!!

Answer 2

isnt it 100 y'' -20 y' + y = 0

Answer 3

oops yes

Answer 4

ok you want a characteristic equation 100 r^2 - 20r + 1 = 0

Answer 5

then?

Answer 6

you have a double root, r = 1/10

Answer 7

ya...then?

Answer 8

If tex2html_wrap_inline96 (which happens if tex2html_wrap_inline98 ), then the general solution is

displaymath64

Answer 9

http://www.sosmath.com/diffeq/second/constantcof/constantcof.html

Answer 10

the general solution is y = c1 *e^(1/10 x) + c2 *x *e^(1/10 x)

Answer 11

is there a way to obtain without memorizing the formula?

Answer 12

not that i know of

Answer 13

there are 3 cases, distinct roots, double roots, and the imaginary roots. its not too bad, there is pattern

Answer 14

the imaginary case is a little tricky

Answer 15

thank you

Answer 16

Can this method also solve differential equations of the form y"=f(x)?

Answer 17

how will u proceed after u take y''=f(x)?

Answer 18

yes it usually makes it easier to reduce the quadratic, except in the case where there are radical linear factors

Answer 19

show that the defferential equation y(y^2+2x)+2x(y^2+x)dy/dx=0 is not exact, but that it has an integrating factor of the form u=x^2y^k for some integer k. hence or otherwise find the general solution of this differential equation