AMath350.F12.A7

# 14 c use the variation of parameters y0 3to solve the

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Unformatted text preview: 3xy 0 3y = 0. 14 c) Use the variation of parameters y0 = 3to solve the equation x2 y 00 +3xy 0 A= and method . 47 2 1 3y = . x 5. Consider the DE y = Ay where 50 A= . 0 of the system y0 = Ay + F(x), where 2. Find the general solution 5 ✓ ◆ ✓ ◆ (a) Show that A has one eigenvalue of multiplicity 2 that has two linearly 21 4xe x . independent A = eigenvectors. 2 , and Fthe general 0 Hence give (x) = solution of the DE. 1 (b) Write the DE in component form, solve the resulting equations and compare your answer with part (a). ✓ ◆ 42 6. Find the general solution the equation 0 ( = Ay + f x) where 3. Find the general solution of of the systemxy t) = Ax+F,(where A = 2 1 ✓ ◆2 1 4xe x 1= A/t , and F(x) = . and f (t) = . 2 0 4 + 2/t 1 7. Consider a commodity with constant supply S = 50 and demand curve 4. Consider a commodity with constant supply S = 50. Suppose the demand whose derivative is given by curve has derivative dD dD 2D 5p + 10 = dtdt = 2D 5p + 10 where D is the demand and is the price. The rate of of increase of price where D...
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