Question
The streamlines of a fluid flow are given by$$\frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{x}{y}$$ Show that $x^{2}+y^{2}=A$ where $A$ is a constant. Sketch the streamlines for $A=1,25$ and 100
Step 1
We are given: $$ \frac{dy}{dx} = -\frac{x}{y} $$ To make this equation separable, we can multiply both sides by $y$ and divide both sides by $x$: $$ y \frac{dy}{dx} = -x $$ Show more…
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ORDINARY DIFFERENTIAL EQUATIONS
Other methods for first order equations
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