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Unformatted text preview: Your signature: (4) Consider the diﬀerential equation 2 xy dy dx = 4 x 2 + 3 y 2 , x > . (a) Use a change of variables to convert the d.e. so that it is separable. You must express the answer in the form f ( u ) du = g ( x ) dx or p ( y ) dy = q ( x ) dx . (b) Solve explicitly for y . Your signature: (5) Solve the following initial value problem: dy dx =x 2 + y cos( x ) sin( x ) + y , y (0) =1 . Your signature: (6) Consider the diﬀerential equation ( x 2 + xy 2 ) y3 xy + 2 y 3 = 0 . (a) Show that the d.e. is not exact. (b) Show that xy2 is an integrating factor. (c) Solve the resulting d.e....
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 Spring '07
 King
 Differential Equations, Equations, Trigraph, Constant of integration, Boundary value problem, Polytechnic Institute of NYU MA

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