I need help on #7, please. 6. Most of the problems considered in the text are li

Question

I need help on #7, please. 6. Most of the problems considered in the text are linear. The equation y' = 1 + y- is nonlinear, and it is easy to see directly that y = tan x s the particular solution for which y(O) = O. Show that by assuming a solution in the form of a power series finding the on' s cnx" and a, by the usual method. Note particularly how the nonlinearity of the equation complicates the formulas. b. by differentiating the oquation repeatedly to obtain (n) co f (o) and using the formula cn 7. Solve the equation y'·x- y, y(0) = 0 by each of the methods suggested in problem 6. What familiar function does the resulting series represent? Verify your conclusion by, solving the equation directly as a first order differential equation.

Explanation / Answer

Y' + y = x

First order differential equation...

I.f = e ^x

Solution of differential equation is ...

Y. e^x = integration of (x.e^x)dx

Y.e^x = e^x(x+1) + c

Solution will be above equation ... answer

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