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3354_f05_t1sol

# 3354_f05_t1sol - equation u = u t t ANSWER u = t(ln t C 1 6...

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Math 3354, Section 2, Test # 1, Name KEY 1. Pure Time Solve the initial value problem u = 3( t + 1) t with u (1) = 1. ANSWER: u ( t ) = 2 t (3 + t ) - 7 2. Exact Show that the equation (1 + u 3 ) + (1 + 3 tu 2 ) u = 0 is exact and use this fact to find an implicit form of the general solution. ANSWER: t + tu 3 + u = C 3. Separable Use the method of separation of variables to find the solution to the initial value problem u = e - u with u (0) = 0. ANSWER: u ( t ) = ln ( t + 1) 4. Separation of Variables Use separation of variables to find the general solution of u = 3 u t + 2 . ANSWER: u ( t ) = C ( t + 2) 3 5. Homogeneous Find the general (nonzero) implicit solution of the homogeneous
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Unformatted text preview: equation u = u + t t . ANSWER: u = t (ln ( t ) + C 1) 6. First Order Linear Solve the ﬁrst order linear equation u = u + e t with u (0) = 2. ANSWER: u = ( t + 2) e t 7. Substitution Use the substitution y = ( u + t ) to ﬁnd an implicit solution of u = ( u + t ) 2-1. ANSWER: ( u ( t ) + t )-1 + t = C 8. Bernoulli equation Find an implicit form of the general solution of the bernoulli equation u = 1 2 u + e t u-1 . ANSWER: u 2 = e t (2 t + C )...
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