Unformatted text preview: dy dx = e y ( y 2-2 y ) . Clasify each point as asymptotically stable, unstable, or semi-stable. By hand, sketch typical solution curves in the regions in the xy plane determined by the graphs of the equilibrium solutions. 5. Solve the following initial value problems (a) x 2 y ′ = 1-x 2 + y 2-( xy ) 2 with y (1) = 0 (b) (1 + x 2 ) dy dx + 2 xy = f ( x ) where f ( x ) = b x ≤ x < 1-x x ≥ 1 with the initial condition y (0) = 0. 1...
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- Fall '10
- initial value, dy, typical solution curves, Initial value problems