Calculus - DifferentialEquations - quiz1

Question 1: What is the solution to the differential equation $y'=y$

y=Ce^(x^2) y=Ce^x y=e^x y=Cx

Question 2: What is the solution to the differential equation $y'=xy$

y=Ce^x y=Ce^(x^2/2) y=Cx^2 y=Ce^(x^2)/2

Question 3: What is the solution to the differential equation $-y''=y$

y=Asin(x)+Bcos(x) y=Ax^2+Bx+C y=Ae^x+Be^(-x) y=Ce^x

Question 4: What is the solution to $y'+2y=0$?

y=Ce^(-2x) y=Ce^(-x) y=Ce^(2x) 2Ce^x

Question 5: What is the integrating factor for $y'+P(x)y=Q(x)$?

∫P(x)dx e^(∫Q(x)dx) P(x) e^(∫P(x)dx)

Question 6: What is the solution to $y'=3y$?

3x y=Ce^(3x) 3Ce^x y=Ce^x

Question 7: What is the solution to $y''−y=0$?

y=Ax^2+Bx+C y=Asin(x)+Bcos(x) y=Ce^x y=Ae^x+Be^(-x)

Question 8: What is the order of the differential equation $y'''+2y''+y'=0$?

2 1 3 0

Question 9: What type of DE is $y'=f(x)g(y)$?

Homogeneous Linear Separable Exact

Question 10: What is the general solution to $y'=2x$?

y=x^2+C y=2x^2+C y=2x+C y=x+C

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