Math, asked by Azaguvel, 5 months ago

The particular integral of (D2 +D)y=x2+2x+4 Is​

Answers

Answered by aditijaink283
6

Given:

Consider the given DE

(D^{2} +D)y=x^2+2x+4

Find:

We have to calculate particular integral PI

Solution:

PI = \frac{1}{D^2+D}(x^2+2x+4)\\\\=\frac{1}{D(1+D)} (x^2+2x+4)\\\\=\frac{1}{D} (1+D)^-1(x^2+2x+4)\\ =\frac{1}{D} (1-D+D^2)(x^2+2x+4)\\=\frac{1}{D}(x^2+2x+4-2x-2+2)\\ =\frac{1}{D}(x^2+4)\\ =\int\limits ({x^2+4} ) dx\\ =\frac{x^3}{3}+4x

Similar questions