Solve the following differential equation using the method of undetermined coefficient coefficients
d^2y/dx^2 + 9y = x^2 cos3x
This was the most difficult assignments i had encounted as this was not taught in our module yet we are required to solve it . what i had learn before are the right hand side x^2 + cos3x but not multiply .
r^2 + 9 = 0
r(r+ 9) = 0
r=+/- 3j
Yc =C1cos3x + C2sin3x
Yp= (Ax^2 + Bx + C) (Dcos3x + Esin3x) ?
why is it Yp= (Ax^3 + Bx^2 + Cx) (Dcos3x + Esin3x) n not Yp= (Ax^2 + Bx + C) (Dcos3x + Esin3x) ?
to solve the equation we need to find yp,yp1,yp2
yp1 differential yp by dx , and yp2 is differential by yp1.
how to solve it,since it will become very complex as Ax^3.Dcos3x =ADx^3cos 3x(2 unkown is inside AD), Ax^3.Esin3x =AEx^sin 3x(2 unkown is inside AE)......... (Rem this is only yp ) still need to solve yp1 and yp2 there will be a lot of unknown .....
is there any simple method ?
aft substutite Yp2 and yp into d^2y/dx^2 + 9y = x^2 cos3x
where we need to find the value of A,B,C,D,E
you can't have your particular solution of the same form as your homogeneous solution. you will just get zero when you plug everything in, which gets you nowhere. to avoid this, multiplying through by x is the standard trick.
no, you need to find yh (the homogeneous solution) and yp. that's itto solve the equation we need to find yp,yp1,yp2
yp1 differential yp by dx , and yp2 is differential by yp1.
what you typed is confusing. anyway, the method of undetermined coefficients says to find , and and plug them into your original differential equation. equate the coefficients to solve for A, B, C, D and Ehow to solve it,since it will become very complex as Ax^3.Dcos3x =ADx^3cos 3x(2 unkown is inside AD), Ax^3.Esin3x =AEx^sin 3x(2 unkown is inside AE)......... (Rem this is only yp ) still need to solve yp1 and yp2 there will be a lot of unknown .....
is there any simple method ?
aft substutite Yp2 and yp into d^2y/dx^2 + 9y = x^2 cos3x
where we need to find the value of A,B,C,D,E