Special Form Of X In Differential Equation

Special Form of X in Differential Equation-1:  Basic special forms of X in differential equation are given as:

Type 4: P.I of the form where V is the function of x.

Hence ( 1 ) reduce to;

Replacing U by V, we get the required results.

Type 5: P.I of the form where V is a function of x.

By leibniz's theorem, we have

∴ Equation 1 reduce to;

This is a formula for finding the particular integral of the functions of the xV. By repeated application of this formula, we can find P.I as x²V,x³V,.........