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Linear first order ODE (Page: 3)

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  1. Integration factor;
  2. Solving \(y\prime = 2xy\) with Integrating factor;
  3. Solving \(y\prime = 2xy\) by separating variables;

Let's solve the same equation \(y\prime = 2xy\) by separating variables and proving that both methods will give the same results.

\[\frac{\mathop{dy}}{\mathop{dx}} = 2xy \]

\[\frac{\mathop{dy}}{y} = 2x\mathop{dx}\]

\[\int\frac{\mathop{dy}}{y} = \int 2x\mathop{dx}\]

\[\ln{\left|y\right|} = x^2 + C\]

\[e^{\ln{\left|y\right|}} = e^{x^2 + C}\]

\[y = Ae^{x^2}\]

As you can see, we have the same answer, which meant that both techniques work perfectly and for some equations it is your choice which technique to use for solving.

For more details on this method, please watch this video:

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Published: 2023-05-14 01:12:52
Updated: 2023-05-14 01:39:32

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