Separable ODE y' + 6xy = 0 with y(0) = 1

Question

Find the solution of $y'=-6xy$ that satisfies $y(0)=1$ .

Short answer

$y=e^{-3x^2}$ . Separate: $dy/y=-6x\,dx$ , so $\ln|y|=-3x^2+C$ ; the initial value fixes the constant to $0$ .

Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 3.5 Ordinary Differential Equations, 'Separable ODE A', p.46; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Separable Equations: Technique and Initial Conditions
Applications: Systems of Linear Differential Equations du/dt = Au