Separable Differential Equation, Help Appreciated
- Thread starter dli42395
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HallsofIvy
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That is, as you say, a "separable differential equation" and looks very straight forward. What difficulty are you having with it?
It can be written as \(\displaystyle 6y\sqrt{x^2+ 1}\frac{dy}{dx}= 9x\) and then as \(\displaystyle 6ydy= \frac{9x dx}{\sqrt{x^2+ 1}}\).
You don't have to but I would automatically divide both sides by 3: \(\displaystyle 2ydy= \frac{3x dx}{\sqrt{x^2+ 1}}\)
Now integrate both sides. If it is the integral on the right, try the substitution \(\displaystyle u= x^2+ 1\)
It can be written as \(\displaystyle 6y\sqrt{x^2+ 1}\frac{dy}{dx}= 9x\) and then as \(\displaystyle 6ydy= \frac{9x dx}{\sqrt{x^2+ 1}}\).
You don't have to but I would automatically divide both sides by 3: \(\displaystyle 2ydy= \frac{3x dx}{\sqrt{x^2+ 1}}\)
Now integrate both sides. If it is the integral on the right, try the substitution \(\displaystyle u= x^2+ 1\)
D
Deleted member 4993
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Subject to the initial condition:.
I realize this is a simple problem. I am actually in calc 2 and my professor just glossed over this.
These are the easiest type - almost like algebra...
\(\displaystyle 9x \ = \ 6y*\sqrt{x^2+1}\dfrac{dy}{dx} \ \)
\(\displaystyle \dfrac{9x}{\sqrt{x^2-1}} dx \ = \ 6y*dy \ \)
Now integrate both sides....