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. y ′ − 2 y = φ ( x), ⎧2, x φ ( x) = ⎨ ⎩0, x < 1 > 1 ( −∞ , +∞ ) y = y( x), ( −∞ ,1) (1, +∞ y(0) = 0. ) φ ( x) , y = y( x) x = 1 y( x) .
x < 1, y′ − 2 y = 2, y ∫ 2 d x − ∫ 2 d = e [ ∫ 2e d x + C1] x 2 x − 2 x = e [ ∫ 2e d x + C1] 2 x = C1 e − 1 ( x < 1) y ( 0) = 0, C 1 = 1, 2 x , y = e − 1 ( x < 1) x > 1, y′ − 2 y = 0, y 2d x 2 x = C 2 e ∫ = C 2e ( x > 1)
Page 1 and 2: , dy = dx 2xy . dy = 2xdx y dy
Page 3 and 4: . k > 0 20 1 tW dW = −kW
Page 5 and 6: . . 1, (1) 0, (0) 1 ] [0, 0) ) ( )(
Page 7 and 8: 1 e . y′ + y = . x x 1 x e P (
Page 9 and 10: dx dy − 1 ⋅ y − x ∫ = y 1 1
Page 11 and 12: y x y x f t y x d d 2 1 2 2 2 4 2 2
Page 13 and 14: . ( t = 0) . v(t), : F = mg
Page 15 and 16: 2. dv m dt = mg − kv dv dt ∫
Page 17 and 18: y ′ + y = 2 3x y [ ] ∫ 2 C x e
Page 19: ϕ( x) 1 −∫ d x sin x ∫ d x =
Page 23 and 24: y′ = cos cos y ysin 2 y − xsin
Page 25 and 26: . Σ > 0 x ∫∫ Σ = − −
Page 27 and 28: f 1 1 ′ x ( x) + ( − 1) f ( x)
Page 29 and 30: . d y = ycos x d x , d y y ∫
Page 31 and 32: . 1, , 1(). , h() t. , dV Q =
Page 33 and 34: − π(200h − h 2 ) dh = 0.62 2gh
Page 35 and 36: . sin x d d y x + ycos x = 5sin x
Page 37 and 38: . yd x + xd y = sin yd y x, y,
Page 39 and 40: . , ) ( 3 ) ( ) ( 2 2 2 2 3 2 2 2
Page 41 and 42: . 12000, 0.1% CO 2 , CO2 , 2000 0
Page 43 and 44: . f ( x) (1) ⎧ ⎨ ⎩ y′ y(
Page 45 and 46: : 2 2 1sec x tan ydx + sec y tan xd
Page 47 and 48: x y 1tan x tan y = C 2( e + 1)( e
Page 49 and 50: . xydx y( 0) = 2 + ( x + 1) dy 1 =
Page 51 and 52: y + d x y . = e . dx − y x 1 e
Page 53 and 54: . 1m , , 2 S = 1cm . , , h t
Page 55 and 56: , π t = − 0.62 2g π = − 0.62
Page 57 and 58: . , y = F ∈C f (x). 1 , ∫ L
Page 59 and 60: dx ⎡ 2 x ⎤ . + − dy = 0 . 3
Page 61 and 62: d i R E t i m sin + = ω d t L L i
Page 63 and 64: . dy dx −1 y 2 + = a (ln x) y . x
Page 65: . 1. f (x) f ( x) x = sin x −

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12.2 å¯åç¦»åéçå¾®åæ¹ç¨ä¸ä¸é¶çº¿æ§å¾®åæ¹ç¨