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Question: differential equations problem 21 please show all work answer is...

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Differential Equations problem. #21, please show all work! (Answer is y^3-3y^2-x-x^3+2=0, |x|<1)

Some of the results requested in Problems 21 through 28 can be obtained either by solving the given equations analytically or by plotting numerically generated approximations to the solutions. Try to form an opinion about the advantages and disadvantages of each approach. 21. Solve the initial value problem y (1 + 3x2)/(3ys_6y), y(0) 1 and determine the interval in which the solution is valid. Hint: To find the interval of definition, look for points where the integral curve has a vertical tangent.
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