Mathematics

$$\frac{dy}{dx}=xy+x+y+1$$


SOLUTION
Given $$\dfrac{d y}{d x}=x y+x+y+1$$
$$\dfrac{d y}{d x}=x(y+1)+(y+1)$$
$$\dfrac{d y}{d x}=(x+1)(y+1)$$
$$\implies \dfrac{d y}{y+1}=(x+1) d x$$
Integrating on both sides
$$\implies \displaystyle\int \dfrac{d y}{y+1}=\int (x+1)d x$$
$$\implies \ln (y+1)=\dfrac{x^2}{2}+x+C$$
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Subjective Medium Published on 17th 09, 2020
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