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HW-2 Solution

# HW-2 Solution - z p x = 1 x A x x x ˙ z p = A x x A x = A...

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aa ) solution ˙ y + y x = xy 2 solution : ˙ y = 1 x y xy 2 Bernoulli ' sEquation a ( x ) = 1 x b ( x ) = x α = 2 z = y 1 α = y 1 ˙ z = y 2 ˙ y plug in ˙ y ˙ z = y 2 1 x y xy 2 ˙ z = 1 x y 1 + x plug in z = y 1 ˙ z = 1 x z + x linear hom ogeneous : ˙ z h = 1 x z h 1 z h dz = 1 x dx ln( z h ) = ln( x ) + C z h = Cx

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a ) continued particular : z p = A ( x ) ( ) x ˙ z p = A '( x ) x + A ( x ) = 1 x

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Unformatted text preview: z p + x = 1 x A ( x ) ( ) x + x ˙ z p = A '( x ) x + A ( x ) = A ( x ) + x A '( x ) x = x A '( x ) = 1 A ( x ) = x z p = ( x ) x = x 2 total : z t = z h + z p z t = Cx − x 2 ⇒ plug − in : z = y − 1 1 y = Cxx 2 y = 1 Cx + x 2...
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