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I'm stuck

  • Thread starter RadiationX
  • Start date
256
0
I need to solve this D.E.

[tex]x^2y''-xy' + y = x^3[/tex]

i'm supposed to use the variation of parameters technique.

in that technique i need to get a coeffecient of 1 in the first postion of y'' and then sove the homogenous D.E.

[tex]y''-\frac{y'}{x} +\frac{y}{x^2}=0[/tex]

the above leads to

[tex] m^2-2m +1=0[/tex]

now solving this i get

[tex]C_1x +C_2tx[/tex]

my problem is that i don't know how to move forward with
[tex]C_2tx[/tex]

how do i proceed
 
Last edited:

dextercioby

Science Advisor
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It's an Euler equation.You need to transform it into a linear equation with constant coeffs.Read the theory again and identify the substitution you need.

Daniel.
 
256
0
do you mean that this is a Bernoulli equation?
 

dextercioby

Science Advisor
Homework Helper
Insights Author
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532
I told u it was/is an Euler eqn.

Make the sub

[tex] x=e^{t} [/tex]

[tex] y(x)\longrightarrow \bar{y}(t) [/tex]

Daniel.
 
Last edited:
256
0
ok. i'll figure it out
 

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