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myrzilka [38]
2 years ago
7

(2x+y)dx+(x-2y)dy=0 solve the differential equation

Engineering
1 answer:
Nonamiya [84]2 years ago
4 0

Answer: y' = - x'

<u>Explanation:</u>

Let f(x) = 2x + y

then f'(x) = 2 + y'

Let f(y) = x - 2y

then f'(y) = x' - 2

Given:  f'(x) + f'(y) = 0

         2 + y' + x' - 2 = 0

                y' + x'= 0

                 y' = -x'

This can also be written as:       \dfrac{dy}{dx}=-\dfrac{d}{dx}

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The thickness of aluminium needed to stop the beam electrons, protons and alpha particles at the given dfferent kinetic energies is 1.5 x 10⁻¹⁴ m.

<h3>Thickness of the aluminum</h3>

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r = \frac{2KZe^2}{K.E} \\\\r = \frac{2 \times 9\times 10^9 \times 13\times (1.6\times 10^{-19})^2}{2.5 \times 10^6 \times 1.6 \times 10^{-19}} \\\\r = 1.5 \times 10^{-14} \ m

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Since the magnitude of charge of electron and proton is the same, at equal kinetic energy, the thickness will be same. r = 1.5 x 10⁻¹⁴ m.

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r = \frac{2KZe^2}{K.E} \\\\r = \frac{2 \times 9\times 10^9 \times 13\times (2 \times 1.6\times 10^{-19})^2}{10 \times 10^6 \times 1.6 \times 10^{-19}} \\\\r = 1.5 \times 10^{-14} \ m

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Learn more about closest distance of approach here: brainly.com/question/6426420

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