3xy + 4y = 0 (x > 0), 4₁(x) 2 is a (6) For the equation z²y" solution. (a) Use the method of Reduction of Order to obtain a second, independent solution. 1

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Q: Use reduction of order method to solve + = 0, given that one solution is g(x)= e. Find first 1/2(t)…

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Q: Find the solution using undetermined coefficient method (0²-1)y = 8x cX 0

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A: To solve the second order ordinary differential equation by fourth order Runge-Kutta method, convert…

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Q: w2 – w + 6 dw w3 + 3w 2.

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: If x=√√ 1-t and y=-3t+1³, what is y'? (Α B (C) D -6 (t-1) (t+1) √√1-t 6(1²-1) √√1-1 -3 (1²-1) √√1-1…

A: x=1-ty=-3t+t3y'=dydx=dydtdxdtdtndt=ntn-1

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Q: 11. In the function y = 3x2 - 3, y is replaced by y and then y is replaced with y +2 ; the new…

A: Given:     Function y=3x2-3   Here y is replaced by 12y       substitute y=12y      12y=3x2-3…

Q: (i) (D² – 4D+ 13) y=e2r 4x (ii) (D² + 16) y=e*

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Q: 4. (D2 + 2D + 1Jy = 6

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Q: 11. The general equation for a family of quadratic functions is y = a(x + 1)(x - 3). Find the…

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Q: 4. Sketch: (a) f(x, y) = 4 – x² – y? f (x, y) = x² – y² + 2x ** (b) (c) f(x, y) = /A– x² – 4y² f (x,…

A: 4. (a) We are to sketch the graph of the function f(x,y)=4-x2-y2 \

Q: 2x- (ii) Given aty=b²x-y and a 4x+3 = bx-5y, show that 3y-6x=7x² +5y²

A: (ii) Given ax+y=b2x-y and a4x+3=bx-5y We will use logarithm properties to solve the given:

Q: In(-/-) (vi) 2x In - x = 0

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Q: Solve for the zeros of the quadratic function f(x) = 9x2 + 6x + 1. Write the answer as a fraction.…

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Q: Solve ylk + 2) + 2yjk + 1} + v[k] = 0 if y[-1] = 1, y[–2] = 1 %3D

A: Given,                            y[k+2]+2y[k+1]+y[k]=0                               ...(1)…

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Q: Find the general solution to y(4) – 6y " + 8y" = 0. In your answer, use c1, C2, C3 and c4 10 denote…

A: The detailed solution is as follows below:

Q: y The solution of y' = 6, y(0) = 2 is 10+x X +x² + 20 (A) 60x + 3x? + 20 (В) 10+x 10+x 3x? (D) +60x…

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Q: 4 Solve y" – y" – y' + y = 2e¬t + te' + 3 by using both the method of undetermined coefficients and…

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Q: Find the general solution of æ²p+ y²q = (x + y)z.

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Q: f(x-1) e-2x+x² dx = O 1 -2x+x² e 2 2e-2+2x+C 2e-²x+x² + C e-2x+x² + C + C

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Q: x2 (4) Calculate the result of the equation Having x= 0 , 1 , 2 /5+ x

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Q: (2k

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Q: xy" + xy² + 4y = /Nx Find the solution y(x)

A: We will find the solution of the differential equations.

Q: Solve MXVN at (1,1-1) When M = (2yz)i – (x²y)j + (xz²)k and N = 2x²yz³ Show the graph after it.

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Q: If r2+ 2r –1 = 0 is the characteristic equation of a homogeneous D.E. with constant coefficients,…

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Q: Write in factored form. Determine the x-intercepts. y = x². - 1

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Q: y? (x² + 1) x(y2 + 1) 4. Solve the IVP y = y(-1) = 3. You may leave your answer in implicit form.

A: We need to solve the differential equation.