Initial Value Problems for Linear Shooting Method

danbone87
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Homework Statement



y''-by'=f(x)

I have to "derive and submit the appropriate initial value problems (with initial conditions) for u(x) and v(x). Show me all 4 equations and initial conditions... "

and I know you get u(x) and v(x) by solving ivp's for the original equation, one homogeneous and one not. but do i use two initial guesses for y'(0)=? and then i have 4 of those? I'm unsure of what is being asked exactly.
 
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danbone87 said:
y''-by'=f(x)

i'm unsure of what is being asked exactly.

So am I. What is f(x), u(x) and v(x) and how are they related?
 
u+av

is a linear combination of y. such that u'(0) = 0 and v'(0)=a
 
whoops, v'(0)=1
 
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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