Microsoft Word - Extra Credit.docx MA 2A Extra Credit 1. Find the general solution for the following equation: (x3 + y3 + 2xy) dx + (3xy2 + x2 + y3) dy = 0. 2. Find the solution of the equation !" !#...

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Microsoft Word - Extra Credit.docx MA 2A Extra Credit 1. Find the general solution for the following equation: (x3 + y3 + 2xy) dx + (3xy2 + x2 + y3) dy = 0. 2. Find the solution of the equation !" !# + 4xy= 2x with y(0) = 2. 3. If y(x) is a solution of y’ = x2 + xy + y with y(3) = 2, find an approximation for y(2.9) using Euler’s method with h = -.05. 4. Suppose y(x) is a solution of y’ = (y - 4)(50 – y) . a. If y(0) = 0, what is the limit of y(x) as x approaches +¥ ? b. If y(0) = 10, what is the limit of y(x) as x approaches +¥? c. If y(0) = 100, what is the limit of y(x) as x approaches +¥? 5. Find the general solution to !" !# = 2y + x + 5. 6. Find the general solution of y’’ = 5y’ + 6y where y is a function of x. 7. Find the solution of y” – 2y’ + y = 0 with y(0) = 3 and y’(0) = -2. 8. Find the general solution of y” = 3y’ +4x -5. 9. Find the general solution to x2y” + 7xy’ + 8y = 0. 10. Find two linearly independent power series solutions about the point 0 to: y” – xy’ + 2y = 0. 11. Find L {f(t)} directly from the definition of the Laplace transform if f(t) = 2t + 1 for t £ 1 and 1 for t > 1. 12. Find L {t5 } 13. Find L {t5 sin 3t} 14. Find L-1{ $%& $'%( } 15. Use the Laplace transform to solve y ′′ − 3y ′ + 2y = e3t , y(0) = 1, y′ (0) = 0. MA 2A Extra Credit 16. Using eigenvalues, find the general solution to the following system of equations. x’ = -6x + 2y y’ = -3x + y 17. Using eigenvalues, find the general solution to the following system of equations. x’ = -6x + 5y y’ = -5x + 4y 18. Using eigenvalues, find the general solution to the following system of equations. x’ = x + y y’ = -2x - y