2. Eliminate the arbitrary constants of the equation below, where B is a parameter. x = c1eßt + c2 e-2ßt Sin 2t -

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Q: Show that the equation dy + 2k possesses solutions of the form 00 -kt E C, e cos (C, x+ E,) cos…

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A: Topic = Differential equation

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Q: x*y"+xy'+(x? y=x cos x 2. Show that is a solution of the equation

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Q: 3. Differentiate the following with respect to the variable: a. y =-2 Lnx – cos 5x + 6 sin 2x – 2 x²…

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Q: 4- find Juw w = X + y y + Z ९ ८०९ ६ y = e Sint and

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Q: Show that the equation dy + 2k possesses solutions of the form E c, e cos (a,x+&,) cos (w,t+ 8,)…

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Q: Show that the equation dy + 2k possesses solutions of the form Σ 2 c, e cos (a, x+ E,) cos (w,t +…

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Q: 2. Eliminate the arbitrary constants of the equation below, where ß is a parameter. x = cjeßt + c2…

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Q: Write an equation of the form y=a sin bx Ol ↑y. BIN 4 4- 2. NAI 3π 37 4

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Q: What is the form of a particular solution of the equation: y" – 6y' + 9y = t² + e* – 4 cos t Do not…

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Q: Eliminate the arbitrary constants of the equation below, where B is a parameter. x = czeßt + c2…

A: Given, x=c1eβt+c2e-2βtSin 2t-4t3 To eliminate the arbitrary constants in the above equation.

Q: B. F (x, y) = 2yi + 3xj * (x, y) = %3D C. F (x, y) = (2 sin y) i+ (-4y+2x cos y) j * (x, y) = Note:…

A: In this question we will use basic of calculus. We will simply find the curl of F to check…

Q: 4- Solution of the following equation 4xy²dx + (x² + 1)dy = 0 is

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Q: 2. Eliminate the arbitrary constants of the equation below, where ß is a parameter. 4 x = C₁eßt + C₂…

A: To find- Eliminate the arbitrary constants of the equation below, where β is a parameter. x = c1eβt…

Q: Eliminate the arbitrary constants of the equation below, where B is a parameter. x = c1ebt + c2…

A: Given, x=c1eβt+c2e-2βtSin2t-4t3 To eliminate arbitrary constants of the above equation

Q: solve the di¡erential equation. 17. y′ = sin^3 x cos^2 y             18. x dy - (x4 - y) dx = 0

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Q: (b) y" – 2y' + 5y = eª cos 2x, y(0) = 2, y' (0) = –1.

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Q: (b) I xy(z +2) dx dy dz

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Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b.…

A: Separable equation:   A first order differential equation y’ = f (x, y) is called a separable…

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

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Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy² 2x3 + x²y +y³ b.…

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Q: W = x =t' +7, y=cos(2t), z=4t COS

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Q: /4 (6) Evaluate I cos y dz dr dy = A. B. C. D. A

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Q: Question 14 Solve the following DE: (2xy? + 3x?) dx + (2x²y+ 4y) dy = 0 O a²y? + 3x + 4y = C O a'y?…

A: Solution of differential equations

Q: 1. x= A sin (wt + 8); w a parameter, not to be eliminated. 2. y= cx + c? +1 3. y? = 4ax 4. y = C1 +…

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Q: 3. Solve: (y? + ry)dr + (5y² – xy + y° sin y)dy = 0

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Q: Find for the equation yz? – et* cos(4zx)-3y² =4 ây

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Q: Find the general solution of the given equation. y" + 36y = 0 Choose the correct solution below. c,…

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Q: 4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

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Q: -Solve b exact (Di sferential Egmation) Q 1- (3X+y Cosx) dx+(stux-uy)dy=o

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Q: Show that the equation + 2k dy =c². possesses solutions of the form 00 2 c, e " cos (a, x + &,) cos…

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Q: Show that the equation dy + 2k possesses solutions of the form 00 Σ C,e -kt cos (a, x + E) cos (w,t+…

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Q: Express = In(4t), y = 7 – t in the form y = f(x) by eliminating the parameter. y =

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Q: Suppose that y1 and y2 are distinct particular solutions to y" + p(t)y' + q(t)y = – sin(t). Which of…

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Q: Solve the following differentinl equations: 1. (x-y-2) dx + (x – 2y – 3) dy = 0.

A: Solution 1: Given that (x-y-2)dx+(x-2y-3)dy=0 we can write it as dydx=-x-y-2x-2y-3             (1)…

Q: Show that the equation dy + 2k possesses solutions of the form 00 - kt E c,e cos (oa,x+ E,) cos (w,…

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Q: If L(ešt + cos(3t)) = As²+Bs+C (s–5)(s²+9) the value of C is

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Q: Show that the equation dy + 2k possesses solutions of the form 00 -kt E C, e cos (C, x+ E,) cos…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.