Q1. Solve the following: (1) 4 - xS 13 (ii) 2(x – 6) + 3x < 8 х, х (iii) z* +=5

Q: 2. Eliminate the arbitrary constant on the given equation: y = C₁e-²x + De4x

A: Given  y=C1e-2x+De4x

Q: 9. Solve d²x dt² + 4x + 5y = 1²; d²y dt² + 5x + 4y = t +1.

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Q: 11. Find the particular solution of 2ydx = 3xdy, when x -2, y = 1

A: Given : Differential equation :  2ydx = 3xdy And x = -2, y = 1   To find : Particular solution of…

Q: 3. Solve 2x²y" + xy' − 3y = 0 with the initial condition y(1) = 1 y′(1) = 4

A: This is a Cauchy Euler equation. The equation is solved by a substitution.

Q: Solve the problem: max/min U = xy subject to x2 + y2 2 %3D

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Q: Q.4 Solve Cauchy Euler DE x³y" + 4x²y" – 5xy' – 15y = x*

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Q: 2. Find general solution of the DE y" + 3y" + 3/ + y = 0

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Q: What is the particular solution for y′=−2e^x−3x^2+x−4 such that y(0)=1?

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Q: Which of the following is true in solving the initial value problem=x³—4—3e³¹,y=1whenx=0 ? A --4x-e³…

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Q: Q4: Use the Gauss-Seidel iterative technique to find approximate solutions to 10x -x +2x3 -x +11x2-…

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Q: 7. Find the value of h(2) given that (ho gXx)= 4x +4x+4 and g(x) =2x + 1.

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Q: 1.Find the roots of the equation f(x) = x³ - x - 1 using xo 1 %3D %3D For 4 iteration by fixed…

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Q: 5. Solve xdx + ydy а? (хdу-ydx) x2+y2 using exact D.E method.

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Q: x" – 2x' + 4x = d(t – 1) x(0) = x'(0) = 0 - -

A: For solving this question we use the table of Laplace transform and properties of Laplace transform…

Q: Solve a & b with given A[r = 3x şax+ (y + z + 3) Ay +(6x - z³) a₂] where: np = ax + 4ay - 2az 2+y³

A: Given

Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

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Q: 11.2) SOLVE : 5x²y" + x (1+x) y ² - y = 6 by Frobenius Method

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Q: 4.2 Apply the appropriate method to calculate the following: 1 = f***-8 I = S x2-4

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Q: 8. Find the solution x (t) of the IVP given as 2" + 4a' + 13x = f (t) x (0) = 0 and a' (0) = 0 }

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Q: B1(b): Solve the initial value problem : f'(x)= x!0 + 12x + 19 and f(0) = 1.

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Q: 1. Eliminate the arbitrary constants on the given equation: y = C1 + C2e¯ -2x 2 Eliminato

A: Given

Q: H4. Use the method of variation of parameters to find the general solution of dy -X- - 3y= 4x³. dr2

A: Please find attachment for the details solution

Q: Solve the following Higher Order Non-homogenous DE using Methods of undetermined coefficients…

A: Given,y'' -2y' +y=3x+2A second order linear, non-homogeneous ODE has the form of   ay''+by'+cy=gxThe…

Q: 9. Solve for y, showing all work: 12x – 4y = 20

A: Using algebraic operation

Q: Suppose that x-y" + axy' + by = 0 has the general solution of the following form: y = C,x³ + C2x³ In…

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Q: Find the general solution of the following using the method provided: 3. Variation of Parameters y"…

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Q: 2. Solve y' = 2x(x² – y), with initial condition y(0) = 1. -

A: This is first order linear differential equation

Q: Find the particular solution determined by the initial condition. P(X) = 2x ° = 3x )= -6 2/5 - 3x:…

A: This belong to initial value problem of differential equation.first we solve the differential…

Q: Solve the following examples 1 2 2xy with the initial condition(1) =1 y3 6.

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Q: [3 Marks] B1(b): Solve the initial value problem : f'(x) = x14 + 12x + 18 and f(0) = 7.

A: To solve the following initial value problem, f'(x)=x14+12x+18 and f(0)=7 f(0)=7 implies that when…

Q: 8. Solve the Cauchy-Euler equation 4x²y" + 8xy' + y = 0.

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Q: x²y = 1+ cx

A: the given equation is x2y=1+cx

Q: Solve the particular solution (D2 + 3D + 5)y = 5e-x sin (2x) using D - operator method.

A: We find the particular solution of  (D2 + 3D + 5)y = 5e-x sin (2x) using D - operator method.

Q: Find f by solving the initial-value problem. f'(x)=6/(x)1/2 , f(1)=19

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Q: Solve the given problem: y'' + 4y= 3sin2x

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Q: (7) Find the general solution to y = (x +y + 1)

A: Given differential equation is: dydx=x+y+1 Let us assume x+y=t 1+dydx=dtdxdydx=dtdx-1…

Q: (4) B/ If Ø = (x³y²z) and A = 2xz 1-3y2j+ 3xy²k Find ?у ?х the point (2, -1, 3)? at

A: Given:        ϕ=x3y2z         A=2xzi^-3y2j^+3xy2k^         ϕA=x3y2z2xzi^-3y2j^+3xy2k^…

Q: 8. Find the particular solution of x²y"+ xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: eular method

Q: 4. Solve Ar, = 3n2 + 4n - 1 with the initial condition r = 3. %3D

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Q: Suppose M(0) is any value between 0 and k = 100. Can we say anything about long term behavior of the…

A: Solution: Given differential equation, dMdt=-rMlnMK

Q: III. Solve the problem 1. x"(t) + x(t) = 6sin2t; x(0) = 3 and x'(0) = 1 2. Given:

A: As per bartleby guidelines we only give first question answers.

Q: S'z xdx (1+x)*

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Q: dy 1. Determine the general solution of x = 2 – 4x3

A: since u have asked multiple question in a single request so we will be answering only first…

Q: 1. Solve the equation on the interval 0s0<2x. 4sin 2e-3=0 O A. 3'3 元 5元 B. 6 6 I 5x 7 11x С. 6 6 t…

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Q: 2.40 Solve the following problem for x (t) and y(t): x = -2x + 5y y = -6y - 4x + 10us (1) x(0)=5…

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Q: 4) To find the root of the equation x2- 6 = 0 by using the fixed point method in [1,2] one of the…

A: Fixed point iteration method

Q: 10. Find the particular solution that satisfies the initial condition. xy'+ 2y = 3x² – 5x. Initial…

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Q: 1 Find the general solution of x'y" +xy' -y= x+1

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