Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 1 - First-Order Differential Equations - 1.4 Separable Differential Equations - Problems: 1

Answer

$ln|y|=x^2+C$

Work Step by Step

Multiply both sides of the equation by $\frac{dx}{y}$. $$(\frac{dx}{y})(\frac{dy}{dx}=2xy)$$ $$\frac{dy}{y}=2xdx$$ Since each side is in terms of one variable, you can integrate. $$\int \frac{dy}{y}=\int 2x dx$$ $$ln|y|=x^2+C$$
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