Separation of Variables (Edexcel A-Level Mathematics): Flashcards

To isolate variables for solving differential equations.

It should be in the form $dy/dx = g(x)h(y)$.

Separate $y$ terms from $x$ terms in the equation.

$\frac{1}{y} dy = x dx$.

Integrate both sides with respect to their variables.

It's $\ln |y| + C$.

It's an arbitrary constant after integration.

Add the constant of integration, $C$.

$y = C_1 e^{\frac{x^2}{2}}$.

It's a solution not explicitly solving for $y$.