Unformatted text preview: substitution y ( x ) = y 1 ( x )+ u ( x ) you can transform a Riccati equation into a Bernoulli’s equation. (b) Find one-parameter family of solutions for the diﬀerential equation dy dx + 2 xy = 1 + x 2 + y 2 knowing that y 1 ( x ) = x is a solution. 4. (a) Find an implicit solution of IVP dy dx = y 2-x 2 xy , y (1) = √ 2 . (b) Write the solution explicitly and give the largest interval I over which the solution is deﬁned. 1...
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- Fall '10
- Equations, Trigraph, Elementary algebra, TheStart