Show that 6r- t= In 2r- is an implicit solution of the DE : dz (6r-1)(1-2r). dt Give the explicit solution and its interval of definition.

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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Q: Find the solution of the equation y= 2x -x- 10 in the interval (2, 4] using derivatives. You can use…

A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

Q: D7 + D® – 2D$ – 2D4 – 7D³ – 7D² – 4D – 4) y = 0 - - - -

A: follow next step

Q: Q/find (2xy? -2x² y4 xy2+2x)dx+(3X=y?e4yldyco an int egratinagfactor theequation and find the…

A: Given the first order differential equation           2xy3-2x3y3-4xy2+2x dx+3x2y2+4y dy=0 Find the…

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Q: a) x2y"+ xy' +(x2- 25)y = 0 b) (1 - x2) y" - 2xy' + 42y = 0 %3D %3D

A: a. Bessel ordinary differential equation has the form of x2y''+xy'+x2-v2y=0. Now, Rewriting the…

Q: Is the given statement true or false? Justify your answer.   'The equation y'=x+y  is separable.'

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Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

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Q: +タ x2 – 1

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Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: Determine the values of x, y and z if (x+y+z)i + (y-z+1)j + (x-z)k=0. (x−y)i + (y+2z)j +…

A: A vector  is equal to the  vector if all the individual components are equal to

Q: (b) Show that general solution of the second-order difference equation: yk+2 - Gyk+1 + 8yr = 2+ 3.k²…

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Q: PLEASE HELP ME ANSWER WITH SOLUTION    18

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Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

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Q: 2. (LI-2) Consider the equation r2y" - xy + y = 0. It is given that y₁ = z is one solution to this…

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Q: 2x+1 10x+5 + dx 2. Show that (* +1)(2-x) x +1 2-x (4x² + 4)(2–x)' . Hence, find

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Q: -4x+2 Integrate f6 dx with respect to x using the substitution method. (-2x2+2a-2) COMPLETE THIS IN…

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Q: Evaluate: (8t3 – 9t2 + 7)dt -

A: Topic = Integration

Q: y₁=1+a3x³ + arº +... Y₂ = x + b₁x¹ + b₁x² + ... Enter the first few coefficients: a3 = a6 = b₁ b7 )…

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Q: What is the value of x in (2x - jy) + (y - jx) = 1 - j5?

A: We have to find the value of x where 2x-jy+y-jx=1-j5

Q: I [20 / (e(8-10x) dx. The integrand equals 20 divided by [e raised to power of (8 - 10x)]. O…

A: ∫ex dx =ex+C

Q: A) B) dx₁ dt dx₂ dt dx₁ dt dx2 dt dx₁ dt dx₂ Wh = x₁ + 2x₂ + 2x₁.x2 = x₁ + x₂-X1X2 is stable or…

A: Given :           A) dx1dt=x1+2x2+2x1x2    dx2dt=-x1+x2-2x1x2           B) dx1dt=-x1+x2+x12…

Q: Use a computer algebra system to analyze the graph of the function. f(x) = 1/x2 -4x-32   Label any…

A: Given function is f(x)=1x2-4x-32 Graph of function is

Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: cln3 dx (b) (10 points) Ф) (10 роints) z et n2 e*-e

A: We use the definition of the integral of functions and partial fractions to evaluate the given…

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A: the given equation of the curve is: y3+y2-5y-x2+4=0 we have to find the value of dydx

Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: OFind the inlagral of : S(725(フスーヴxりー23x +4ズ)(1-4で

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (b) For the solution that satisfes v(0)1, sketch the solution curve and estmate the following v(0.5)…

A: (b) The solution that satisfies y(0) = 1 can be sketched as follows:

Q: Solve (1) 5-3x 2. (2) 4. 2 3 y-31 y-5 2 5 (3) 2. 4 4)

A: since we answer only first three sub-parts so we will answer first three. Please resubmit the…

Q: Write the following equation in the form w = u(x,y) + iv(x,y) h(z) = (3z + 2i) / (2z2 + 4)

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