Solving Differential Equations with Substitution Method

der.physika
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I'm having trouble setting up this solution can anyone give me a hint, or set it up, so I can see if what I'm doing is right?

xy\prime=y=e^x^y

using the substitution

u\equiv(xy)
 
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xy\prime=y=e^x^y

What do you mean with two = in "equation"?
 
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Sorry about that, I wrote that wrong the actual problem is

xy\prime+y=e^x^y

using the substitution

u\equiv(xy)
 
Last edited:
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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