2xyy’=x^2+y^2 | Homogeneous first order ODE | Math 02/08
In this lecture, I will solve the 2xyy’=x² + y² homogeneous first-order differential equation. I will show how to convert this equation to a canonical form y’=Q(y/x) but will do a solution via substitution without using a canonical form of this homogeneous ODE.
For this type of homogeneous differential equation, I will always recommend not using the final formula for solving, rather than substitution in the original equation and following all steps accurately – this will allow you to avoid a lot of errors.
M̲̲y̲ l̲e̲c̲t̲u̲r̲e̲s̲:
▶ Math / 02 – ODE (I): • Math / 02 - ODE (I)
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▶ Text version: http://mycoding.uk/a/solving_2xyy____...
Lecture content:
0:00 – 2*x*y*y’=x² + y²
0:17 – Canonical form y’=Q(y/x)
1:17 – Substitution y = v*x
2:54 – Integration
5:50 – Final solution
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#differentialequations #ode #differential_equation