HYE FRIENDS M1 IS A SCORING SUBJECT .SO IN ORDER TO GOOD MARKS IN THIS SUBJECT THIS BLOG PROVIDES U A GIST OF IMPORTANT TOPICS.

LINEAR DIFFERENTIAL EQUATION WITH CONSTANT COEFFECIENTS

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

LINEAR DIFFERENTIAL EQUATION OF SECOND AND HIGHER ORDER

AN EQUATION OF THE FORM
dⁿy∕dxn+p1(x)dn-1y∕dxn-1+p2(x)dn-2y∕dxn-2+………pn-1(x)dy∕dx+pn(x)y=x
dny/dxn+a1dn-1y/dxn-1+a2dn-2/dxn-2+………an-1dy/dx+any=x

where p1(x),p2(x)………..pn(x) and x are all functions of ‘x’ is called the linear differential equation of order n.