Unformatted text preview: y = e x +2 x sin( y )+3 y 2 +3 Solution Write y as dy dx , multiply both sides of the equation by (sin( y ) + 3 y 2 + 3) dy and take antiderivative, we have Z sin( y ) + 3 y 2 + 3 dy = Z e x + 2 xdx Now using Mathcad or compute by hand, we ﬁnd Z sin( y ) + 3 y 2 + 3 dy =-cos( y ) + y 3 + 3 y + C and Z e x + 2 xdx = e x + x 2 + C So we have an implicitly deﬁned solution y ( x ) by the equation-cos( y ) + y 3 + 3 y = e x + x 2 + C Here, we can’t ﬁnd an explicit formula for y ( t ) . a Practice...
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.
- Spring '11