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Differential Equations2D

Exact & Linear Differential Equations - Theory & Concepts - Exact And Linear Equations

Solving First-Order DEs using Exactness, Integrating Factors, and Linear Methods (including Bernoulli's Equation).

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Linear DE

y' + \frac{2}{x}y = 4x

Find an integrating factor $\mu(x) = x^k$ to make it exact.

Select power $k$

k

0.0

✗ Not Exact

\mu(x) = x^{0}

\frac{d}{dx}\mu(x)

P(x)\mu(x)

To be exact, we need $\frac{d\mu}{dx} = P(x)\mu(x)$ . Match the blue curve to the dashed red curve.

First-Order DEs (Separable & Homogeneous) - Theory & Concepts - First Order Separable And Homogeneous Applications of First-Order DEs - Theory & Concepts - Applications Of First Order Des Higher-Order Homogeneous DEs - Theory & Concepts - Higher Order Homogeneous Equations Higher-Order Non-Homogeneous DEs - Theory & Concepts - Higher Order Non Homogeneous Equations