Verify that the function y = x2 + 2x + C (explicit or implicit) i… - Vidyadip

Question

Verify that the function y = x² + 2x + C (explicit or implicit) is a solution of differential equation y' - 2x - 2 = 0

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Answer

Given: y = x² + 2x + C ...(i)
To prove: y is a solution of the differential equation y' - 2x - 2 = 0 ...(ii)
Proof:From, eq. (i),
y' = 2x + 2
L.H.S. of eq. (ii),
= y' - 2x - 2
= (2x + 2) - 2x - 2
= 2x + 2 - 2x - 2 = 0 = R.H.S.
Hence, y given by eq. (i) is a solution of y' - 2x - 2 = 0.

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