Finding complementary function from roots r=0,1 in variation of parameters

[s7b]

Hi,

When using the method of variation of parameters to solve something like;

y'' + y' = 2^x

I got the aux. equation: r^2 - r =0 which gives the roots r=0,1

How do I find the complementary equation yc?

 

[ice109]

what is the aux. eqn? did you solve the homogenous eqn by assuming an exponential then differentiating and plugging in?

 

[matematikawan]

Hi,

When using the method of variation of parameters to solve something like;

y'' + y' = 2^x

I got the aux. equation: r^2 - r =0 which gives the roots r=0,1

How do I find the complementary equation yc?

If you meant complementary function then it got nothing to do with the method of variation of parameters. The method is meant for computing a particular solution y_p(x).