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5. Solve the following Bernoulli equation; dy y = 2ce y2 dx with the initial condition 9(0) 2, using an appropriate substitution_...

Question

5. Solve the following Bernoulli equation; dy y = 2ce y2 dx with the initial condition 9(0) 2, using an appropriate substitution_

5. Solve the following Bernoulli equation; dy y = 2ce y2 dx with the initial condition 9(0) 2, using an appropriate substitution_



Answers

Find the solution of the differential equation that satisfies the given initial condition.
$ x + 3y^2 \sqrt {x^2 + 1} \frac {dy}{dx} = 0, y(0) = 1 $

Hello, everyone. Today we're going to solve problem number 47 for wireless plus 38 square y equal to X square like you so unequal toe three Q equal toe X square peak orto three x squared So right to the power minus two Mhm integral minus two three X square DX, which is equal to integral minus two extra square A to the power minus two in the three x Square DX Hindu B X This one is integrating factor, So why do they get things like virus to minus two in tow? The power minus two F cube equal toe violence integral two X square into the par minus two X cube the x So right praise to minus two equal toe one by three plus C into the power to execute one day right square equal toe one by three plus e into the power to excuse. Thank you

Okay, Part A. We know that we can do the question role so one times X minus one minus X plus one times one over the denominator squared. Remember the formulas F one G minus After you won over G squared The simple question negative, too. Over X minus one squared and then we can write a D ax. After this. Maybe wanting to part B. We have negative two over two minus one squared times 0.5 gives us t y equals negative 0.1.

Hello, everyone. Today we're going to solve problem number. So for here they given the question is why? Why you guys minus two ways square equal toe into the power X So he integral minus four. The eggs equal toe either the power minus four X toe white square in tow. Power minus four X equal to integrate toe the politics into the par minus for X the X So why it's square equal toe either. Apart for X integral to the par minus three x the x so white square equal toe into the part for X Indignant to you know the poor minus three x the x through wife square, equal toe into the part for its minus two It'll a par minus three x by three plus c So by square, equal toe see, you know the part for its Linus to buy three into the bar X Thank you


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