SKEDSOFT

Maths For Engineers - 2

Special Form of X in Differential Equation:

Type 2: P.I of the form  

We have D ( Sin ax) = a cos ax

Therefore, if f (D2) is a rational integer function of D2 then f(D2) sin ax = f(-a2) sin ax.

Hence,

     

 f ( - a2) ≠ 0

Similarly we can provide that,

The formula can be easily remembered as follows:


Type 3: P.I of the form Φx/ f(D) where Φ(x) is a polynomial in x, we seeking the polynomial equation as the particular solution of :

   f (D)y = Φ (x)

Hence P.I os found by divisor. By writing Φ (x) in decending power of x and f(D) in ascending power of D. The division get completed without any remainder. The quotient so obtained in the process of division will be particular integral.