Differential equation x dy dx =1,y(1)=0 Function y= - Vidyadip

Question

Differential equation $\text{x}\frac{\text{dy}}{\text{dx}}=1,\text{y}(1)=0$

Function $\text{y}=\log\text{x}$

✓

Answer

Here, y = logx

Differentiating it with respect to x,

$\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}}$

$\text{x}\frac{\text{dy}}{\text{dx}}=1$

so, y=logx is a solution of the equation

If $\text{x}=1,\text{y}=\log1=0$

so,

y(1) = 0

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