The complementary function(C.F.) of the differential equation (D – 8)² (D + 4)y = 8x is_ - O (c. + c_x)e®8æ + c,e° -4x O (c1 + c2x)e¯ (c1 + C2x)e¬8¤ + C3e¬4® (cı + c2x)e¬8¤ + cze% O (c1 + c2x)e$e + C3e%®

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: Please see the answer in step 2

Q: Form the partial differential equation by elimaniting the constants form z=axey+1/2 a2e2y+b

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Q: Discretize the differential equation y" – 2y' + 4ty = 2t, y(-1) = -2, y(0) : -2 with step-size h %3D…

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Q: 6) ( y - 2xy ) dx + 3x'dy - 0 ; y( 2) = -1

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A:

Q: Show that each of the functions defined in (A) is a solution of the corresponding differential…

A: To check the solution first check order of Differential Equation and no. Of arbitrary constant in…

Q: Convert the differential equation u'' + 5u'+ 3u = letting x = u, y = u' et into a system of first…

A: We need to convert the differential equation u"+5u'+3u=e2t …........ (1) into a system of…

Q: = 3 dt? Find the solution of the partial differential equation- by variable separable method

A: given ∂2z∂x2=3∂2z∂t2 to find- solution of p.d.e using variable separable method solution let z=xt be…

Q: Investigate the solution of the second order differential equation d²v + (4 × 10-6)v = 0 dt2 dv with…

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Q: Exercise (2): Determine whether the differential equation is linear or nonlinear: (1) (1- )y" - 4ry…

A:

Q: Determine the solution of the differential equation d5x ,d*x d3x d2x + 12 + 8 - ds5 ds4 ds3 ds2 а. x…

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Q: Transform the given differential equation into an ferential equations. equivalent system of…

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Q: Find three linearly independent solutions of the given third-order differential equation and write a…

A: Given equation is: y'''+3y''-6y'+2y=0 Then the auxiliary equation is: m3+3m2-6m+2=0

Q: Czsin(2x) + C4cos(2x) y= C¡sin(x)cos(x)+ C2sinh2x+ is the general solution of which of the following…

A: Here, we have the general solution : y=C1sin(x)cos(x) +C2 sinh (2x) +C3 sin(2x)+C4 cos(2x)ex…

Q: Solve the differential equation (2x + y) dx - O a. 5x+10y + In |10x O b. O c. 5x O d. 5x (4x + 2y -…

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Q: Determine the solution of the differential equation 2y"-3y' + 4y = 0 3x V23 y = e (C, cos x+ C2sinx)…

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Q: Obtain the solution to the differential equation: (3x²y² + 2y³)dx + (2x³y + 6xy²)dy = 0 x³y² + 2xy³…

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Q: Determine the solution of the differential equation ex y" – 2y' + y = 1+x2 - y = C,e* + C2xe* +÷e*…

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Q: The characteristic equation of the differential equation 2 y (4) + 11 y (3) + 18 y " + 4 y' - 8 y =…

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Q: The general solution to the differential equation - 2 ()- is dr = 0 is | dt3 dt2 dt O x = C1 + C2e +…

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Q: Transform the given differential equation into an equivalent system of first-order differential…

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Q: Verify that y1(x) =cos2x and y2(x) =3(1−2sin2 x) are solutions to the differential equation y′′+4y =…

A: Given : the differential equation is, y''+4y=0  and two function defined as, y1x=cos2x  and…

Q: Form the differential equation for the function 2xy= asin2x -bcos2x O a. xy" +2y' = – 4xy O b. xy"…

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Q: Determine whether the given first-order differential equation is linear in the indicated dependent…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relatio y…

A: From the given problem: y=Ae4x+Be7x....(1) Now finding: y'=dydx=dAe4x+Be7xdx=4Ae4x+7Be7x..2…

Q: Form the Differential equation if its solution is V=acos(2x +b) O a. y'= 2x b. None of these O c.…

A:

Q: - Show that the partial differential equation = 0 has the general solution u(x, y) = e"[f(x) + g(y)]…

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Q: If the auxiliary equation associated with a homogeneous linear differential equation with constant…

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Q: What is the auxiliary equation associated with the second order linear differential equation d^2x…

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Q: Solve the partial differential equation = 3, u(x,0) = 7edz by the method of separation of variables.

A: Solution

Q: Use order reduction to find the solution of the differential equation. 4x²y"+y= 0; y, = x² In x 1/2

A: Let y1(x) be non-trivial solution of differential equation y''+p(x)y'+q(x)y=0 and let…

Q: Determine the total solution of the differential equation (D²+8D+16)y = 64cos4x. OA.y = C₁e(-4x) +…

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Q: Find the solution of the differential equation that satisfies the given initial condition. dP 7VPt,…

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Q: The formation of the partial differential equation by eliminating arbitrary function of z = 5f(x" –…

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Q: Transform the given differential equation into an equivalent system of first-order differential…

A:

Q: What is the auxiliary equation associated with the second order linear differential equationd^2x…

A: We need to find auxiliary equation.

Q: The differential equation 3y(x -1dx+(x³ +8y– 3xdy = 0; is exact because OM ON %3D

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Q: The general solution of the differential equation x²y" – 2y = Inx - is O C1x² + c2x¯+ In x 1 4 -2x…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A:

Q: Determine whether the statement "The differential equation y′ = xy − 2y + x − 2 is separable" is…

A: Determine whether the statement "The differential equation y′ = xy − 2y + x − 2 is separable" is…

Q: Determine the solution of the differential equation d5x -7 ds5 d*x d³x + 12 ds4 d²x + 8- = 0 ds² ds3…

A:

Q: Form a differential equation from y =c(x' +2), here c is arbitrary constant. %3D а. dy (x² + 2) –…

A: y = c(x3 + 2)    ..............................(1) differentiation w. r. to x dydx = c3x2 + 0dydx =…

Q: Discretize the differential equation y " – 3y' – y = -3t, y(-1) = 0, y(1) = 0 with step-size h %3D

A: Given: y''- y' - y =-3t, y(-1)=0 and y(1)=0 with step-size h =25

Q: Form the differential equation for the function 2x-y = asin(2x - b) O a. y" + 4y = 8x O b. y" +y = x…

A:

Q: Determine the solutions of the 1st-order linear differential equations below: (a) (x +3y)− x y′ = 0

A: Explanation of the answer is as follows

Q: What are two linearly independentsolutions of the differential equation y''-5y'-6y=0

A: We have to find linearly independent solutions of the given differential equation.

Q: btain the differential equation of the given family of curve: y^2=x^3/(c-x) O A. x^3 y^'+x^2 y+y^3=0…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.