Differential Equations Practice Test: answer key

Every answer, with a link to its step-by-step solution

#	Answer	Lesson	Solution
1	A Yes	Check a solution	Solved step by step
2	A Yes	Check a solution	Solved step by step
3	y = 2x³ + C	Integrals as solutions	Solved step by step
4	y = 23e^3x + x + 43	Integrals as solutions	Solved step by step
5	y = Ae^x²	Separable equations	Solved step by step
6	y = Ae^{1 over 3x³ + x}	Separable equations	Solved step by step
7	y = 3e^x²	Separable equations	Solved step by step
8	y = −1/(2x + 1)	Separable equations	Solved step by step
9	A 674.93	Growth and decay	Solved step by step
10	5223.39	Growth and decay	Solved step by step
11	B 45.75	Newton's law of cooling	Solved step by step
12	t ≈ 8.32	Newton's law of cooling	Solved step by step
13	y = 2 + Ce^−2x	The integrating factor	Solved step by step
14	y = −3 + Ce^x²	The integrating factor	Solved step by step
15	D y(0.3) ≈ 1.362	Euler's method	Solved step by step
16	y(2) ≈ 3.3125	Euler's method	Solved step by step
17	y = e^2x + e^3x	Second order	Solved step by step
18	y = −e^−x + 2e^−x2	Second order	Solved step by step
19	y = 2e^3x + xe^3x	Second order	Solved step by step
20	y = 2e^−3x + xe^−3x	Second order	Solved step by step
21	1s	The Laplace transform	Solved step by step
22	6s³ − 4/(s − 5) + 2s	The Laplace transform	Solved step by step
23	f(t) = 1	The inverse Laplace transform	Solved step by step
24	f(t) = e^2t − e^−3t	The inverse Laplace transform	Solved step by step
25	y = 3e^−2t	Solving with Laplace	Solved step by step
26	y = 2e^2t − 2e^−t	Solving with Laplace	Solved step by step

Grade

Count your right answers and divide by the number of questions: A 90% or more, B 80%, C 70%, D 60%, F below 60%.