Question

The particular integral of (D² +1)y = sin2x​

Answer 1

PI. =( sin2 x)/( D^ 2+1)

= (sin2 x)/(-4+1)

= ( sin2 x)/(-3)

Step-by-step explanation:

D^2. = -a^2 where a=2

Answer 2

The particular integral of $(D^{2} +1)y = sin2x$ is $y_{_{PI}} = \frac{-1}{3} sin2x$

Step-by-step explanation:

Given: Differential equation $(D^{2} +1)y = sin2x$

To Find: Particular Integral of the given differential equation

Solution:

• Finding the particular integral of the given differential equation

The particular integral can be determined by considering the given differential equation. Therefore,

$\Rightarrow y = \dfrac{1}{D^{2}+1} sin2x$

Now, using the rule $\dfrac{1}{f(D^{2})} sinax = \dfrac{1}{f(-a^{2})} sinax$ in the above differential equation, we can write,

$\Rightarrow y = \dfrac{1}{-(2)^{2}+1} sin2x$

$\Rightarrow y = \dfrac{1}{-4+1} sin2x$

$\Rightarrow y = -\dfrac{1}{3} sin2x$

Hence, the particular integral of $(D^{2} +1)y = sin2x$ is $y_{_{PI}} = \frac{-1}{3} sin2x$