Verify that the function y = Ax (explicit or implicit) is a solut… - Vidyadip

Question

Verify that the function y = Ax (explicit or implicit) is a solution of differential equation $xy' = y\left( {x \ne 0} \right)$

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Answer

Given: y = Ax …(i)
To prove:y given by eq. (i) is a solution of differential equation $xy' = y\left( {x \ne 0} \right)$…(ii)
Proof: From eq. (i)
y' = A(1) = A
L.H.S. of eq. (ii)
= xy' = xA = Ax = y = R.H.S. of eq. (ii)
$\therefore$ given by eq. (i) is a solution of differential equation $xy' = y\left( {x \ne 0} \right)$.

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