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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

[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

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