The eigenfunctions for y"-2y + Ay = 0, y(0) = 1, y(1) = 0 are O {e I sin ()}, n-1 O {e² sin(")}, TLTI 00 O {e* sin(nrz)} 1 00 O {e 2* 00 sin(nn2)},1 O {e 2# sin()}, 100 Sn 1 SI O {e "sin(nrz)} 1 O {e2" sin( )} O {e2" sin(nnr)},"

Q: The eigenfunctions for y"- 2y' + Xy = 0, y(0) = 1, y(1) = 0 are o {c* sin(nrx)} 1 o {e sin(")}-1 100…

A: First condition should be y(0)=0, from the given answer there is no option such that y(0)=1.

Q: 3/2 x+3/2 x² - 2 Show that dx = In 3.

A: Since there are multiple questions posted, we will answer the first question posted (4). If you want…

Q: The orthogonal trajectories of y = ce5z where c is arbitrary constant. is_ O z+ 2C = 5y O -2x + 2C =…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: At least one of the answers above is NOT correct. The system of first order differential equations:…

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Q: The general solution of the fourth-order differential equation y() + y" +y"-0 is: y=c_1 +c_2…

A: The given differential equation is y(4)+y'''+y''=0 ................................... (1)  Let…

Q: 2) Which of the following is a separable differential equation obtained by applying the appropriate…

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Q: Which one of these equations is not separable? (1) xy' = y ln |x| (2) y' = In y' (3) = x + sin(x)…

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Q: One solution of a 2nd order homogenous LDE is e2*sinx. What is its general solution?

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Q: Which of the following statements is correct for the differen tial equation 1 2 y'+÷y =-x²(cos.x)y²?…

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Q: Show that each of the functions defined in Column I is a solution of the corresponding differential…

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Q: Determine the solution of the differential equation y" - 2y' + y = 14 y = C,e + C,xe" +e* In(1 + x)…

A: First we find complimentary function then find particular integral then solution.

Q: 1) The hyperbolas 6² x ² - a²y² = a) xyy" + x(y²) ²³²- yy²=0 b) xyy" - x (y² 7² - y₁² = c) xyy" - x…

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Q: d tet dx 1+e* , xe" + e* – e 2x A (1+e*)? xe" +e* +e2« B (1+e*) 2 xe* + e2* (1+e*)? (1+e*)xe* – ¢2«…

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Q: Solve the differential equation, e* + 2e*y = 1 dx a) O (x^2)*e^(-2x) b) O (x^2)*e^(2x) c) O…

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Q: Determine the solution of the differential equation shown using Laplace and Inverse Laplace…

A: Given y'''−y=4e−x+3e2x.....1 When, x=0, y=0, y'=−1 and y''=2 Take Laplace transformation of equation…

Q: The implicit solution of the differential equation (1+ x) dy = (1+ y')dx by using variable separable…

A: The answer and detailed explanation is given below-

Q: 1) xy' + (1-x)y = xex

A: As per our guideline we are supposed to be answer only first question,you can repost other question…

Q: The complementary function(C.F.) of the differential equation (D – 6) (D² + 6²)y = e&" is_ cie0a +…

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Q: 7- I = [sec(2x) tan(2.x)dx cos(2x) 8- I = dx 4-sin (2x) csc (In(x)) 9. I: dx

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Q: Between any two real roots of the equation e* sin x-1=0, the equation e* cos x+1=0 has (a) at least…

A: Between any two real roots there is a one root of its derivative.

Q: Find a general solution of each reducible second-order differ- ential equation yy" = 3(y')2

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Q: Hence find a general solution of the equation 2 1 w" () - ¹ ()² = ² 2. w' w'

A: We have to find the general solution of the equation It is given that  and

Q: Consider the nonlinear time-dependent ordinary differential equation (ODE) y '(t) = y ^2 (t)+…

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Q: 3.b) Eliminate the Ar bitrary Constants in the equation: ( 3.a) Eliminate the Arbitrary Conat anta…

A: We have to obtained differential equation of given curves.

Q: (2xe" + e*)dx + (x² + 1)e'dy = 0

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