2) FIND THE GENERAC SOLUTIO OF THG ODE 2y +2y +y = 0

Q: For the ODE dy = y² – 3y dt find a(yo) for Yo < 0 O 00 -V3 O V3

A: Answer

Q: 1. Determine the equivalent ODE by eliminating arbitrary constants y = ae-2x + bxe-2x Oy" +4y' + y =…

A: Given data:- y=ae-2x+bxe-2x

Q: A second order Caushy – Euler equation having a solution y(x) = x-cos(4Inx) is O x²y" + 5xy' + 16y =…

A:

Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: 3. Given the ODE = 3x2- x²y ; y(2) = 5. Find the second order Taylor dy dx polynomial for y as a…

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Q: What technique should you use to solve the ODE that arises from the Euler's equation associated with…

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: tody + y² = 0 dt

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Q: Q2= A) for E= 2xĭ-3Y3+K %3D prove That divc curl È)=0 %3D

A:

Q: 59. By the transform method, solve Utt = Urx +h, 0 0, h = constant, Ut (x, 0) = 0, 0 0. u (x, 0) =…

A: We use Laplace transformation method to solve the given partial differential equation. Also use…

Q: For the ODE = y² – 3y dt .2 find w(yo) for yo < 0 3 V3 O-V3

A:

Q: t2 and y2 3 are two distinct solutions of the IVP t²y" – 4ty + 6y = 0, The functions yi %3D y(0) =…

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Q: az Suppose z is a function of r and y, and csc Vr² + yz = 2"e»in z_ Solve for dz and dy

A: Given: csc x2+yz=zyesin x To find ∂z∂x and ∂z∂y.

Q: Let H(x)=0∫x√4−t^2 dt, for −2≤x≤2. a) Evaluate H(0) b) Evaluate H'(2) c) Use geometry to evaluate…

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Q: 55. By the transform method, solve Ut = Urx + g (x,t), u (x, 0) = f (x), 0 0, 0 0.

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Q: sinz Calculate Rz-4|<T z(z-R)² dz using Residue Theorem. |z-4|<n z(z-n)²

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Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 2. z = In(2x² + y); x = /i, y = 12/3…

A: Given: z=ln(2x2+y);  x=t , y=t2/3To find:dzdt=??

Q: -8 6. Evaluate the integral +y² dydx

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Q: Find the horizontal asymptote of f (z) = 8z-822-240z 3z-3z2-60z Section 3.4 Oy = %3D Oy = 4 Oy= Oy =…

A: Solution-

Q: Solve the ODE: xy"+2y'-xy Oby using the Frobenius method.

A: Given that ODE: xy''+2y'-xy=0                    .....1 We know that the solution to this ODE is:…

Q: f indd Pm in tev ms of @m-l and @gtl n+l -ax dx m,n-1 dx I. Cm, m-l= Hint: Recursive Method Matrid…

A:

Q: Solve this ODE using the Frobenius Method x*y"+x°y'_2y = 0

A: In the Frobenius method we will start by assume a solution of the form  y=xk∑n=0∞anxn

Q: Find the linearization of y = eV3x at x = 64. %3D (Use symbolic notation and fractions where…

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Q: Solve the following difference equation using z-transform. Yn+2 + 6yn+1 + 9yn = 2" %3D Yo = y1 0

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Q: Using the Method of Undetermined Coefficients, a suitabie choice for the nonhomogeneous solution yw…

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Q: (b) Integrate the function f 1 dx by using substitution and partial fraction. x(2x -1) Hence, show…

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Q: Solve the linear first-order ODE y' + In(x) y = xe3, a> 0, where the prime stands for differei with…

A: Given: y'+ln(x)y=x-xe3x

Q: Solve each of the foiiowing ODES 1. (3x?y + 4x°)dx + (x³-ycosy-siny)dy = 0 2. (4x³y3 + 6xy²)dx +…

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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Q: a) Exaluate: %3D :(?)6 puo (x puif (9 and (3 +x x <O %3D for which f (x)=9). Give exact working out…

A:

Q: 3. (a). Use Laplace transforms and partial fractions to solve y" +4y=8t, y(0)=3, y'(0) = 0.

A: Given  y''+4y=8t, y0=3, y'0=0

Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: Use the method of Laplace transforms to solve the symbolic initial value problem y" + 4y = 8(t – 3),…

A: The solution is given below

Q: dx secx + 1 Transforming S Ⓒ 1 +²2² A 1-z² (В) / z²+z 1-z² 2-2z² © 1+z² -z² Ⓒ S 1=32/2/dz D 1+z² -dz…

A: Solve using miscellaneous substitution

Q: Find y2 using Reduction of Order xy" – 3xy' + 4y = 0 , %3D

A: Given differential equation x2y''−3xy'+4y=0....1 Given a solution y1=x2 We have to find the y2 We…

Q: 5. Test the ff ODE for exactness and find the general solution of the DE (2x + 3y) dx + (3x + 4y)…

A: To solve Differential equation.

Q: 1 - Show that u(X, y) - e^Cosy is harmonic function = e and Find tne Conjugate harmonic v(X,y) and…

A: Harmonic function

Q: D. Multiple Choice 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)],…

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Q: Example H-W:_for f(x,y) = cos(xy) – x³ + y* compute fxyy, fxxyy %3D

A: We have to find the partial derivative

Q: 4y" – 9y = 0

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Q: 2. Use Laplace transform to solve with y (0) y" + 4y = 8(t)- 8(t - 2π) 0 and y' (0) = 0.

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Q: For the ODE dy — Зу — у? dt 2 - find a(Yo) for Yo < 0 V3 -/3 3

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Q: 4) Find Yp, using D-operator, where Yp (e). %3D (D+1) (D-2)

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Q: Find the general solution of the folowing ODE: dy -3x² e¯4y dx x³ + C y = - 4 y =In(**÷C) 4 y =1n(x³…

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Q: %3D I+ ylz

A: Given differential equation is ddxyy'(y')2+1-(y')2+1=0                 (1) Since we know that…

Q: ← Z 3 Z (ancosno) z (ansinno) = z (z-a cose) Z-2axwoso ta azsing Z² 2ax cose + a²

A: Introduction: Z-transformed is significant transformation in mathematics. In many fields, it has…

Q: 2. Use Laplace transform to solve with y(0) = y" + 4y = = 8(t)- 8(t - 2π) 0 and y' (0) = 0.

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Q: finde general Sonotion 1- y' = See'y 2X-1 %3D 2- 3-Xy=Y+2x $ in?

A: This question can be solved by applying the concept of differential equation.

Q: 3. Solve the difference equation by using Z-transform Yk+22Yk+1+Yk = Uk, (k > 0) with yo = y₁ = 0,…

A:

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.