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Unformatted text preview: problem is certain to exist. ( t1)(9t 2 ) y + 4 ty = cos(7 t ) , y (0) = 83 Same diﬀerential equation, but with initial condition y (2) = 8. EXISTENCE & UNIQUENESS THEOREM, GENERAL FIRST ORDER CASE Statement on page 70, Theorem 2.4.2. EXAMPLE. State where in the typlane the hypotheses of the General First Order Existence and Uniqueness Theorem are satisﬁed for the diﬀerential equation y = ln  ty  1t 2y 2 EXAMPLE. Verify that both y 1 ( t ) = 1t and y 2 ( t ) =t 2 / 4 are solutions of the initial value problem y =t + ( t 2 + 4 y ) 1 / 2 2 , y (2) =1 . Discuss! HOMEWORK: SECTION 2.4...
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 Spring '08
 Fonken
 Differential Equations, Equations, Uniqueness Theorem

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