For solving frac{dy}{dx} = (4x + y + 1),the s | vedclass

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Question

(D) To solve the differential equation $\frac{dy}{dx} = 4x + y + 1$,we observe that the right-hand side is a linear function of $x$ and $y$.Let $v = 4

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$y + 4x + 1 = v$

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(D) To solve the differential equation $\frac{dy}{dx} = 4x + y + 1$,we observe that the right-hand side is a linear function of $x$ and $y$.Let $v = 4x + y + 1$.Differentiating both sides with respect to $x$,we get $\frac{dv}{dx} = 4 + \frac{dy}{dx}$.Thus,$\frac{dy}{dx} = \frac{dv}{dx} - 4$.Substituting these into the original equation,we get $\frac{dv}{dx} - 4 = v$,which is a variable separable differential equation.Therefore,the suitable substitution is $y + 4x + 1 = v$.

For solving $\frac{dy}{dx} = (4x + y + 1)$,the suitable substitution is:

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