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DIFFERENTIAL EQUATIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDIFFERENTIAL EQUATIONS2 Marks
Question
In each of the verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: $\text{y} = \text{x}^2 + 2\text{x} +\text{C}\ :\ \text{y}' – 2\text{x} – 2 = 0$
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Answer

Given: $y = x^2 + 2x + C .....(i)$
To prove: $y$ is a solution of the differential equation $y' - 2x - 2 = 0 .....(ii)$
Proof: From eq. $y' = 2x + 2$
$\therefore \text{L.H.S}.$ of eq.$(ii),$
$y' - 2x - 2 = (2x + 2) - 2x - 2$
$= 2x + 2 - 2x - 2 = 0 = \text{R.H.S.}$
Hence, y given by eq. $(i)$ is a solution of $y' - 2x - 2 = 0.$

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