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प्रश्न
Differential equation \[x\frac{dy}{dx} = 1, y\left( 1 \right) = 0\]
Function y = log x
उत्तर
We have,
\[y = \log x...........(1)\]
Differentiating both sides of (1) with respect to x, we get
\[\frac{dy}{dx} = \frac{1}{x}\]
or,
\[x\frac{dy}{dx} = 1\]
It is the given differential equation.
Thus, \[y = \log x\] satisfies the given differential equation.
Hence, it is a solution.
Also, when \[x = 1, y = \log 1 = 0, i.e., y\left( 1 \right) = 0\]
Hence, \[y = \log x\] is the solution to the given initial value problem.
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