First slide

Methods of solving first order first degree differential equations

Question

$If \frac{dy}{dx} = y + 3 > 0 and y (0) = 2 then y (\log 2) is$

Moderate

A

-2
B

7
C

5
D

13

Solution

$\int \frac{dy}{y+3} = \int dx \to log(y+3)=x+c$
$\begin{array}{l} y (0) = 2 p u t x = 0 \\ \log 5 = c \\ \to \log (y + 3) - \log 5 = x \\ \to \log (\frac{y + 3}{5}) = x \\ \frac{y + 3}{5} = e^{x} \\ \to y = 5 e^{x} - 3 \\ y (\log 2) = 5 e^{\log 2} - 3 = 5 \times 2 - 3 = 7 \end{array}$

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