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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- Fall '05
- Math, Elementary algebra, Boundary value problem, general solution