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Here is what I would consider writing if I were a student in Cheat Sheet – Differential Equations © Variable Separable Form dy dx = F(x).G(y) Solution Separate the variables: dy G(y) = F(x)dx Integrate both sides:∫ dy G(y) = ∫ F(x)dx Reducible to Variable Separable Form dy dx = f(ax + by + c) Solution Substitute ax + by + c = t ⇒ a + b dy dx = dt dx Convert the equation: 1 b (dt dx − a) = f(t) Separate the variables: dt bf(t) + a = dx Integrate both sides: ∫ dt bf(t) + a = ∫dx … Two distinct real roots. $\Delta>0$.

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It is generally covered after area under curves. Differential Equations are one of the direct applications of indefinite and definite integrals.