First slide

Methods of solving first order first degree differential equations

Question

The slope of a curve at any point on it is the reciprocal of twice the ordinate at that point. If the curve passes through (4,3) then its equation is $lo g(y/3)= \frac{x}{2} -k$ then k is

Moderate

Solution

$\begin{array}{l} \frac{d y}{d x} = \frac{y}{2} \Rightarrow \int \frac{d y}{y} \Rightarrow \int \frac{d x}{2} \Rightarrow \log y = \frac{x}{2} + c \\ Passes through (4, 3) then \\ \log 3 = \frac{4}{2} + c \Rightarrow \log 3 = 2 + c \\ \Rightarrow c = \log 3 - 2 \\ \to \log y = \log 3 - 2 + \frac{x}{2} \\ \Rightarrow \log (y / 3) = \frac{x}{2} - 2 \end{array}$

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