1.Determine the value of a, if any, for which all solutions tend to 0 as t → co. y" - (3a + 7)y' + (2a² + 11a +12)y = 0. ysert yove

Q: Which of the following is a proper substitution for the following Bernoulli's equation 3 e-3x y 2x³y…

A: We have to find the substitution for the given Bernoulli's equation.

Q: 1 [4]y= Cq cos 2x+C2 sin 2x+ (1– xsin 2x) 2

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Q: 8. Solve the ff DE y" -9y = 0 y = c₁e³x + c₂e-3x y = c₁ cos 3x + c₂ sin 3x y = ³x (c₁ cos 3x + c₂…

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Q: Express the equation r = 3 cos 0- 12 sin 0 in Cartesian coordinates. (x² + y²) – 3r + 12y = 0 + y²)…

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Q: Find a particular solution to y" + 8y' + 16y : -7.5e 4t t² +1 Yp =

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Q: Which of the following equations cannot be solved using the method of undetermined coefficients y"…

A: Method of Undetermined Coefficient:

Q: I. Write down the form of the particular solution for the g(x). y" +p(x)y' + q(x)y = g(x) 1. g(x) =…

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Q: If y = cos ¹ prove Zyy + z = 0. )Z = (1 + i)(2-1)-¹, find |Z|.

A: Here given y=cos-1(z/x). We prove that zyy+z=0.

Q: Find the formulation of a particular solution of y" + 3y' +2y = 3+t2 – te-2t cost without…

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Q: a) m - 1 b) m – 2 Q.8) The characteristic equation for y"" + 3y" – 4y = 0 , is : b) 2' = 32?-4 c) m…

A: To find out the characteristic equation.

Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0

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Q: Oy" +3y + 2y = (1+x) (1 – ¤) O y" +3y +2y = 2 sin a cos r %3D (e +e =) 2y" +3y + 5y = %3D Oy" +2y +…

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Q: on of y" – 2y' + 2y =

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Q: 7 sin(2t) + 4 cos(t) = 0 %3D

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Q: The solution of (e® + 2xy²) dx + (2 cos 2y + 2æ?y) dy is given by (A) e + x²y² + cos 2y = c (B) e+…

A: Answer:- The solution of ex+2xy2dx + 2cos 2y + 2x2ydy          —       (1)

Q: Determine the general solution to (D² + 4)(f) = sin(2x) satisfying the initial condition: f (0) = 0,…

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Q: Find the formulation of a particular solution of y"+2y'+ 5y = t² +4t – t²e-t cos 2t without…

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Q: In which form should one look for the particular solution of y" − 2y + 2y = x²eª cos(x) (you do not…

A: Given DE is  y"-2y'+2y=x2excos(x) ......(1) We find form of particular solution of DE (1).

Q: (a) f = (b) f = (c) f = (d) f = (e) f e²t 3e2t [4e-4t [2e51] est est cos(t) e³ sin(21) 20 A 1 43

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Q: Exercise 2. Solve, for z, the equation Inz = 4 – 3i. Exercise 3. Show that (a) sin z = sin 7: (b)…

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Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

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Q: Assume y=ex cos(3x) is one of the solutions of DE (3)-3y" + 7y-5y=0.Then a + B is:

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Q: 3. y" - 2y' = ex (x² + 2) cos2x 4. y" - 2y' - 3y = 4x - 5+ 3xe ²x

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Q: 5. Verify that the following is a Bernoulli equation and find its general solution: 3/ - x² = Y =…

A: To verify that the following is a Bernoulli equation and to find its general solution. x3y'y-x2=-y3…

Q: What is the particular solution of (Dª + 4D² – 1)y = 44sin3x O a. cos3x O b. cos2x O c. sin3x O d.…

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Q: V. Find the general solution of the following Bernoulli's Equation. 1. cosysin2xdx + (cos²y –…

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Q: xy" – y' + xy = 0, t =

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Q: Eval uate the general Solution of the diflerential epation y° (tx + 9)² 2y' t y tanx COS X (4x+s) +…

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Q: The values of m for which y = x" is a solution of x² y" – 7xy' + 12y = 0 are (Select the correct…

A: As the given value of Y is the solution of the equation that's why the value of Y should satisfy the…

Q: Which of the following is a general solution in implicit form? A B C D y=ccosx y=In(cosx+B) + C y =…

A: topic- differential equation Any solution in the form y=y(x) is in explicit form. solution in any…