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Differential Equations Exam Test Bank Questions With Correct Detailed Answers

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DIFFERENTIAL EQUATIONS EXAM TEST BANK QUESTIONS WITH CORRECT DETAILED ANSWERS (y^2 + yx)dx - (x^2)dy = 0 - Answer-homogeneous 1/2x^2 + x/y = c (x+y)dx + (x)dy = 0 - Answer-homogeneous c = 1/2x^2 + 1/2ln(2(y/x)+1) (y^2 + yx)dx + (x^2)dy = 0 - Answer-homogeneous c = ln(x) + 1/2ln(y/x) - ln((y/x)+2) dy/dx = (y-x)/(y+x) - Answer-homogeneous -1/2ln((y/x)^2 +1) - tan^-1(y/x) = ln(x) + c dy/dx = (x + 3y)/(3x + y) - Answer-homogeneous Ln((y/x) + 1) - 2ln((y/x) - 1) = Ln(x) + c (x)dy/dx + y = 1/y^2 - Answer-Bernoulli's (y^3)= (1/3x^-2/3 + c)/(x^1/3) dy/dx - y = e^x(y^2) - Answer-Bernoulli's e^x(1/y) = -1/2(e^2x) + c dy/dx = y(xy^3 - 1) - Answer-(e^-3x)(y^-3) = xe^-3x - 1/3e^-3x + c (x)dy/dx - (1+x)y = xy^2 - Answer-Bernoulli's 1/y = (-e^x(x+1) + c)/(xe^x) (x^2)dy/dx - 2xy = 3y^4 y(1) = 1/2 - Answer-Bernoulli's 1/y^3 = ((-9/5)x^5 + 19/5)/(x^6)

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DIFFERENTIAL EQUATIONS EXAM
TEST BANK QUESTIONS WITH
CORRECT DETAILED ANSWERS
(y^2 + yx)dx - (x^2)dy = 0 - Answer-homogeneous

1/2x^2 + x/y = c

(x+y)dx + (x)dy = 0 - Answer-homogeneous

c = 1/2x^2 + 1/2ln(2(y/x)+1)

(y^2 + yx)dx + (x^2)dy = 0 - Answer-homogeneous

c = ln(x) + 1/2ln(y/x) - ln((y/x)+2)

dy/dx = (y-x)/(y+x) - Answer-homogeneous

-1/2ln((y/x)^2 +1) - tan^-1(y/x) = ln(x) + c

dy/dx = (x + 3y)/(3x + y) - Answer-homogeneous

Ln((y/x) + 1) - 2ln((y/x) - 1) = Ln(x) + c

(x)dy/dx + y = 1/y^2 - Answer-Bernoulli's
(y^3)= (1/3x^-2/3 + c)/(x^1/3)

dy/dx - y = e^x(y^2) - Answer-Bernoulli's

e^x(1/y) = -1/2(e^2x) + c

dy/dx = y(xy^3 - 1) - Answer-(e^-3x)(y^-3) = xe^-3x - 1/3e^-3x + c

(x)dy/dx - (1+x)y = xy^2 - Answer-Bernoulli's

1/y = (-e^x(x+1) + c)/(xe^x)

(x^2)dy/dx - 2xy = 3y^4 y(1) = 1/2 - Answer-Bernoulli's
1/y^3 = ((-9/5)x^5 + 19/5)/(x^6)

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