Solve the differential equation with constant coefficients

Fatima Hasan
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Homework Statement



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Homework Equations



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The Attempt at a Solution


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Is my answer correct?
 

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How do you get √56? Shouldn't it be (√52)/4 = (√13)/2?
 
mjc123 said:
How do you get √56? Shouldn't it be (√52)/4 = (√13)/2?
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Is it correct now ?
 

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Looks OK to me.
 
Fatima Hasan said:
View attachment 234491
Is it correct now ?
1. In the future, please post questions about differential equations in the Calculus & Beyond section. I will move the ones you have posted in the Precalc section.
2. You don't need to ask us to check your work for these kinds of problems. Just substitute your solution in the original diff. equation.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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