

Differential Equations and Initial Conditions
Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
+2
Standards-aligned
Ethan Morris
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in solving the given differential equation?
Apply the chain rule
Differentiate both sides
Use the quadratic formula
Rewrite y' as dy/dx
Tags
CCSS.7.EE.A.1
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which method is used to solve the differential equation in this problem?
Integration by parts
Partial fraction decomposition
Laplace transform
Separation of variables
Tags
CCSS.7.EE.A.1
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the integral of 8y with respect to y?
8y^2 + C
4y^2 + C
8y + C
4y + C
Tags
CCSS.HSA.REI.A.2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the general solution form for y after integration?
y = ±√(1/8 x^2 + C)
y = ±√(8 x^2 + C)
y = ±√(4 x^2 + C)
y = ±√(x^2 + C)
Tags
CCSS.8.EE.A.2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the negative square root not considered in this problem?
Because x is always positive
Because the equation is linear
Because y is always negative
Because y(4) = 5 is positive
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the initial condition y(4) = 5 help determine?
The integral of x
The derivative of y
The particular solution
The general solution
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of C when using the initial condition y(4) = 5?
C = 2
C = 5
C = 23
C = 25
Tags
CCSS.HSA-SSE.B.3B
CCSS.HSF-IF.C.8A
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