Area of the form
dny/dxn+a1dn-1y/dxn-1+a2dn-2/dxn-2+………an-1dy/dx+any=x
where a1,a2,……….an are real constants and x is a function of ‘x’
is called an ordinary differential equation of order ‘n’ with constant
coefficients the above equation can be written in the operator form as.
Dny+a1Dn-1y+a2Dn-2y+…………an-1Dy+any=x
i.e., where D=dy/dx ……………….Dn=dn/dxn
(Dn+a1Dn-1+a2Dn-2+……….an-1D+an)y=x
The complete solution of the above eq is y=complementary function +particular function
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