The solution of the nonhomogeneous DE y" – 2y' +1 = 3e3x is y = cqe* + c2xe* + 3x y = cqe2x + c2 + 0.5x+ e3x

Q: t²y' + 2ty - y³ = 0

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Q: Solve the DE (6x + y2) dx + y (2x - 3y) dy = 0. Hint: Exact O 3x^3 + xy^2 - y^3 = c O 3x^2 - xy^2 -…

A: Given differential equation:- 6x+y2dx+y2x-3ydy=0

Q: Find two linearly independent solutions of 2x²y" - xy' + (−3x + 1)y = 0, x > 0 = x¹¹ (1 + α₁x + a₂x²…

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Q: ӨР dt -10-(0²-81), 0(0) = 1000

A: dθdt=-10-6θ2-81Initial condition : θ0=1000

Q: The top and bottom margms Op a poster are are 8 cm and Hhe Side mary Ms'are each 6 cm if Hhe ae a of…

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Q: Q1// Use Tow Phase method to solve the Mathematical model * (Stop at Table 1 in Stage Two) MinZ=x,-2…

A: Given -  Min Z = x1 - 2x2S.T :x1 + x2 ≥ 2-x1 + x2 ≥ 1           x2 ≤ 3x1, x2       ≥ 0 To find - Use…

Q: solve the deq by method of substituiton

A: The given differential equation is 2x+y+4dx+x-2y-2dy=0......(1) We shall solve the differential…

Q: 30. E=2*10^5 I=30000 L=600 W=25 y = dy dx = W 120EIL 3 (-x ² + 21³x² - (^x) W 120EIL (-5X² +…

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Q: Find the solution of the D.E. xydx - (x2 + 3y?) dy = 0 Show your solutions on a separate sheet of…

A: Given differential equation is xydx - (x2 + 3y2)dy = 0

Q: 2y4-6x3 +|1x=-37x-16 dx X3 - 3x2+5x-I5 2x

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Q: Q4/ In a mass-spring-damper system, the acceleration x₁ (m/s²), velocity x₂ (m/s) and displacement…

A: We are to solve for x_1 , x_2, x_3

Q: y" + 4y' = 3sin2t + tcos2t %3D

A: The solution for the above question is as shown below.

Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

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Q: The solution to the IVP (x² + y²) y'+xy=0 with y (0) = 2 is y (2x²-y)=4. y²(2x² + y²) = 16. Oy²(2x²…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Q1// Use Tow Phase method to solve the Mathematical model * (Stop at Table 1 in Stage Two) MinZ=x,-2…

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Q: E=2*10^5 I=30000 L=600 W=25 y = dy dx W 120EIL = 120 FIL (-5X² + 6(³X²-1²) ū assume as р 38, P = =…

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Q: (c) Consider the double integral || xy dA where D is bounded by the x-axis and the upper half…

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Q: Use the Complimentary-Particular solution in combination with the inverse D-operator to find the…

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Q: Consider the DE dy/dt = y^(3)*(y −1)2(y + 2). Draw the phase line and a graph showing the long-term…

A: This is a problem of the autonomous differential equations.

Q: b) y(4) + y(3) – 7y(2) – y' + 6y = 0. c) y(4) – y(3) – 7y(2) + y' + 6y = 0.

A: Solve the given differential equation Here I am giving answer of 1 st problem if you want answer of…

Q: Solve the IVP 22 + 1ox+1 %3D y Co) =0, y'(0) = -6 Osi ng the quasi-polynomial method.

A: y''-3y'-4y=0 D2-3D-4=0 D2 -4D+D-4=0 (D+1)(D-4)=0 D=-1,4 Complementary function =c1e-x +c2e4x

Q: If the general solution is \( y=c_1x^{-2}+c_2cos(2lnx)+c_3sin(2lnx), \) the Cauchy-Elera equation is…

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Q: DE dx dt = x² - 4x + 3. (a) Its stable critical point is X = unstable critical point is X =

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Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

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Q: Obtain two linearly independent solutions valid near x = 0  x(1 - x)y" - 3y' + 2y = 0

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Q: Exercise 7 Find the general solution 1. 6y'dx - x(2x + y)dy = 0

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Q: Find the annihilator:  f(x) = cos(2x) +4sin (3x)  a. (D^2 +3)^2  b. (D^2 +9)(D^2 +4) c. D^2 - 4D…

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Q: The particular solution (yp) of the equation y" - 3y + 2y = 5 e* is yp = -5xe*

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Q: Use l'Hopital's rule to evaluate the following limits 1+cos(re *) (a) lim, »0 sin(x) In(x-1) (b)…

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Q: xy5 = zy"+yx²

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Q: Obtain general solution of the D.E. y + (1/3)y = e'y A) 1/x = e (c - 3x) B 1/y³ = e* (c - 3x) 1/y =…

A: The given equation is Bernoulli equation we will solve this by substitution method

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.