Calculus - DifferentialEquations - quiz1

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

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

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

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

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

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

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

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

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

P(x) $e^(∫Q(x)dx)$ $e^(∫P(x)dx)$ ∫P(x)dx

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

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

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 $y'''+2y''+y'=0$?

1 2 3 0

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

Homogeneous Linear Exact Separable

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

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

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