Write the values of $D x$ and $D$ for the equation $2 x + 3 y = 4$

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Solution

$2 x + 3 y = 4$

$\frac{d}{d x} (2 x) + \frac{d}{d x} (3 y) = \frac{d}{d x} (4)$

$2 + 3 \frac{d y}{d x} = 0$

$2 = - 3 \frac{d y}{d x}$

$\frac{d y}{d x} = - \frac{2}{3}$

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D

7 x - 5 y = 2

{(\frac{d y}{d x})}^{4} + 3 y (\frac{d^{2} y}{d x^{2}}) = 0

\frac{d^{2} y}{d x^{2}} + 4 \frac{d y}{d x} + 3 y = 3 e^{2 x},

\frac{d^{2} y}{d x^{2}} + 3 y = - 2 x

For the given differential equation find the general solution.

$\frac{d y}{d x} + 3 y = e^{- 2 x}$

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