Quiz 3&4 (1)22

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Feb 20, 2024

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Quiz 3 r.’ (D Correct answers are hidden. Score for this attempt: 10 out of 10 Submitted Sep 19 at 8:47am This attempt took 10 minutes. Question 1 dx . The autonomous differential equation X~ DG+ 1) has a solution that is A Select the correct answer. Increasing 1f V increasing if X > 1
Question 2 dP 1fa>b and 5>0, the autonomous differential equation Py P(a—bP) has a solution that is Select the correct answer. increasi everywhere increasing a increasing if 0 <P < s decreasing everywhere | Question 3 In the autonomous differential equation Select the correct answer. = lis arepeller is an attractor 1 is an attractor dt x(1-x), the critical point = il
[ i Question 4 xe’ The differential equation ¥" S Select the correct answer. Bernoulli linear homogencous separable B T 1/1pts Question 5 (x =), k is a constant, is also a solution. This statement is 1), then y,(x) s differential equation = dx I£y(x) s a solution of an autonomo 1/1pts Question 6 Solve he differential equation - =y(x+1)*
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Question 7 1 y= , ©is a constant Rier T, € is a constant = ¢, ¢ is a constant Yy =c,cis a constant ¢ is a constant 22—y
B sl Question 9 An ordinary differential equation in which the independent variable does not appear exphicitly is known as Equilibrium Variable Separablc i Attractor Autonomous
& et et L SRR Question 10 dy 1 Find an explicit solution of the differential equation —— = 3 P g ax 1+sinx No such solution exist . Quiz 4 (@ Correct answers are hidden. Score for this attempt: 14 out of 17 Submitted Sep 19 at 5:21pm This attempt took 23 minutes. Question 1 The differential equation ¥’ =2y +sin x is Select the correct answer,
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Question 2 The solution of the differential equation ¥ =x¥ is Select the correct answer.
Question 3 The solution of the differential equation 3"~y = Select the correct answer, Y==x=1+ce*
Question 4 An imcgraling factor for the linear differential equation Select the correct answer. 0
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s Question 5 The solution of the differentia] €quation ¥ Select the correct answer, s, =ce
Question ¢ The differential equation 2ty +(x24 1 Jay=0 is Select the correct answer, exact with solution x% tyte exact with solution 2zy . 4 4 exact with solution
- Question 7 pig \ The differential equation Xy + (2 +y3dy =0 is Select the correct answer. not exact but hay Ing an integrating factor x not exact but having an imcgrating factor e€xact with solution —— + 2_ _ €xact with solution —
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e | Question 8 | The differentia] equation 2xydx + (12 +}’3}lf.)" =0 Select the correct answer., | homogeneous Separable exact linear Bernou|jj
| | Question 9 The differential equation ( +2y)dx +ydy =0 can be solved using the substitution Select the correct answer. it cannot be solved using a substitution
Question 10 The differential equation ¥~ Select the correct answer. ¥ X 3 ¥~ can be solved using the substitution
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Question 11 The differential equation ¥’ = (4x+2y+3)? has the solution Select the correct answer. 4x+2}'+3=fi!u[2fix+c]
Question 12 The differential equation ¥ = v/x+y+1 1 has the solution Select the correct answer, T q.cstion 13 Which of the following s A
I cstion 14 Which of the followi tatements best describe the differential equation xdy = y(x —y)d ©)This is a homogencous differe Question 15 & Solve the given differential equation @ = sin(x+y) by using appropriate substitution i @G +y)=sec(x +y) =x +¢
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Question 16 Find the value of so that the ((° + byt —2x)dx + (3yy 2 +20x%3)dy = Odifferential equation D . cstion 17 Which of the fc 1 . o llowing statements is(are) true concerning the differenti equation 2y = —+cosk 4 +3ysin3r =0 b. This is an exact differential equation

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