Eliminate the arbitrary constant. y = C1e-x + C2ex + C3e2x , where y(0) =0, y’(0) = 1, y”(0) = 2

Q: The differential equation (4x2y2 + 6x y )dx + (5x3y + 8x2)dy = 0  has an integrating factor of the…

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Q: Determine the differential equation that is satisfied x2 + y2 + 2ax + 2by + c = 0

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Q: Solve using separable differential equations dy X dx y2V1 + x

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Q: Find the differential equation such that y(x) = c,(x– 1) 2+czln(x – 1)(x– 1)

A: we will eliminate the variables by differentiating

Q: What is the differential equation of the family of circles with their centers on the y – axis and…

A: The given problem is to find the differential equation of the family of circles with centres on…

Q: solve the differential equation dy/dx=2x^4sqrt of y, y.0

A: Solution of given question is written in below steps.

Q: Determine the form of a particular solution to the nonhomogeneous differential equation by the…

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Q: Solve the differential equatons (7x-ty +16) dy + (2x-5y+12) dx=o when x-3, y= 2

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Q: What is the differential equation of the family of lines whose sum of the intercepts is fixed as k ?…

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Q: 5. Find the differential equation of the family of straight lines with slope 1. с. у -130 d. y' +1=0…

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Q: What is SN of the differential equation (2y2 + 3xy – 2y + 6x ) dx + x (x +2y- 1) dy 0 ?

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Q: Find the Homogeneous Differential Equation of: (x2-xy+y2)dx + xydy=0

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Q: Find the function satisfying the differential equation y' - 5y = 2e* and y(0) = 0. %3D y =

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Q: 5. Verify that y(x) = Vx+C is a solution of the differential dy dx 1 for every constant C. equation…

A: The differential equation is given as dydx=12y2ydy=1dx

Q: Find the order and degree of exy" - 3(y¹)² + 2xy = xe^ and write the differential equation in noxmal…

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

A: The differential equation given is as follows y''+y'+4ty=δt-32, y'0=2, y'3=-2 The central difference…

Q: the differential equation 3(3x^2 + y^2)dx - 2xydy = 0 is homogeneous of what degree?

A: The given homogeneous differential equation is 33x2+y2dx-2xydy=0.

Q: (6x + y²) dæ + y (2x – 3 ) dy = 0 is a variable separable differential equation. -

A: Variable separable differential equation is any differential equation that can be written in the…

Q: Use the procedures developed in this chapter to find the general solution of the differential…

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Q: Find the solution of the first order differential equation with the given initial condition: y…

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Q: 2. Solve the nonhomogeneous differential equation, using the basic rule: y(2) + 6y(1) + 9y =…

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Q: Use variation of parameters to find the general solution of the differential x²y" - 5xy' + 5y = 4x…

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Q: find the degree of the differential equation y''-12cosec y= 0   3 1 4 or 2

A: The order of the differential equation is 2.

Q: Find the solution of the Differential Equation: * y(x³y³ + 2x² – y) dx + x³(xy³ – 2) dy = 0; when x…

A: y(x^3y^3 + 2X^2 - y)dx + x^3(xy^3-2)dy=0; x=1, y=1

Q: find the differential equation of y'' + 5y' + 6y = 0 when y (0) = -1, y' (1) = 3

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Q: The differential equation (-xysin x+2ycos xdx +2xcos x dy 0 is

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Q: Find the differential equation of the family of parabolas with vertex ar Focus on the x-axis * O y =…

A: We have to find

Q: Use the method of variation of parameters to find a particular solution of the differential equation…

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Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal.…

A: Differential equations

Q: In the differential equation (2x+3y-5)dx+(3x- y-2)dy=0, the lines 2x+3y-5 =0 and 3x- y-2 =0…

A: This question can be solved using the concept of solving two linear equation.

Q: Solve the differential eqution y'-y=7e^x

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Q: Show that the solution curves of the differential equation y(2x3 – y3) dy x(2y3 – x³) dx are of the…

A: Given equation is Homogeneous differential equation of 1st order.

Q: Find the indicated particular solution of the differential equation. dy dx + 7y= -2e - ⁹x; x = 0…

A: Topic = Differential equation

Q: An integrating factor for the linear differential equation Y' - 2y = 12x is l=

A: The given differential equation is y'-2y=12x. Clearly, the given DE is a first order linear…

Q: Discretize the differential equation y" – y' + 4ty = 5(t + ), y'(-2) = 0. y'(1) = 0 with step-size h…

A: Using center difference method, we can approximate y' and y" as follows.…

Q: Let y' – 35y = 7x*e5x. Is this differential equation pure-time, autonomous, or nonautonomous?

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Q: Obtain the differential equation of the family of curves, parabolas with vertex and focus on the y…

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

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Q: Consider the function y=4e^rx+7 where r is some real number. If y satisfies the differential…

A: In this question we have to find the value of r.

Q: Solve in the form y =f(x) the differential equation  (x+1)dy/dx=(x+2)y given that y=2 and x=1

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Q: Find the terminal value, lim y (r), for the solution of differential equation dy + 3z'y - 6z". dr

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Q: (axy + x² + x4 ) dx – (1 + x²)dy = 0

A: Use linear differential equation condition

Q: gmmuany. Solve the differential equation d²y + 4y = 4tan2x by the method of variation dx2 of…

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Q: Q3: if y'-f(y/x) where v-y/x Find a solution to the differential equation 2xyy'-y2+x2 =0 ?

A: Given

Q: Find the differential equation of a family of parabolas with an axis parallel to the x-axis. O y"y"…

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Q: Determine the form of a particular solution to the nonhomogeneous differential equation by the…

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Q: For the differential equation y' = 2y - x, draw line segments representing the slope field at the…

A: Given that, y' = 2y - x dy/dx = 2y - x At the point (1, 2) we get: dy/dx = 2(2) - 1 dy/dx = 4 - 1…

Q: Solve the differential equatons (9xy-2y2) dx - ( 6x²_xy) dy =0 4.

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Q: Verify that the function y = C1ex + C2e2x is a solution of the differential  equation y” – 3y’ + 2y…

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