Question

(d2+5d)y=x2+7x+9 solve ​

Answer 1

Answer:

Step-by-step explanation:

This is second order linear differential equation with constant coefficients

Characteristic Equation is  m2+5m+4=0   m=−1,−4  

Characteristic Function C.F  =  Ae−x+Be−4x  

Particular Integral  P.I   =  1D2+5D+4  (  x2+7x+9)  

=  14(1+D2+5D4)−1(  x2+7x+9)  

=  14(1−D2+5D4+(D2+5D4)2−...)  (  x2+7x+9)  

=14(  x2+7x+9−  14(2+10x+35)+  116(50))  

P.I  =132(8x2+36x+23)  

General Solution  y=C.F+P.I  

∴   y=  Ae−x+Be−4x+  132(8x2+36x+23)