Subjects differential equations

Separable Equation

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Separable Equation


1. The problem asks whether the differential equation $$\frac{dy}{dx} = y + 3$$ is separable. 2. A differential equation is separable if it can be written in the form $$\frac{dy}{dx} = g(x)h(y)$$, allowing us to separate variables as $$\frac{1}{h(y)} dy = g(x) dx$$. 3. In this equation, $$\frac{dy}{dx} = y + 3$$, the right side is $$y + 3$$, which depends only on $$y$$ and not on $$x$$. 4. We can rewrite it as $$\frac{dy}{dx} = 1 \cdot (y + 3)$$, where $$g(x) = 1$$ and $$h(y) = y + 3$$. 5. Since it can be expressed as a product of a function of $$x$$ and a function of $$y$$, the equation is separable. 6. Therefore, the answer is **True**.