Find x for which the line tangent to the parabola y = 4x – x2 is horizontal.

Q: y" – 5y" + 4y' = e' – 2t

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Q: Find a general solution to the differential equation. y' + 2y = 2 tan 2t - 3t 21-11e³1

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Q: Determine whether the function y = 3 sin 2x is a solution of the differential equation y(4) − 16y =…

A: Consider the given differential equation:

Q: solve xdx+ydy=a^2(xdy-ydx)/(x^2+y^2) using exact Differential Equation

A: Given equation is x dx+y dy=a2x dx-y dyx2+y2.

Q: Solve for the solution of the differential equations below using substitution method by homogenous…

A: Given differential equation is2xydy=x2dx+2y2dxy1=1

Q: Determine the form of a particular solution (without computing the coefficients) to the differential…

A: The given differential equation is y''-14y'+49y=3te7t

Q: у" — 8y 3D 0, у(0) %3D 4, у'(0) %3D5 and y"(0) —D 7

A: We have to solve

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

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

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Q: The differential equation of y = 35Ax – 8B is %3D - dy dx 35 %3D dy da %3D dy da? dy dz2 = 8

A: We can find the differential equation as below

Q: Use the method of reduction of order to find a second solution of the differential equation xy" − y'…

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Q: The order and degree of the differential equation representing the family of parabolas y = 4a(x-h)…

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Q: Use the method of Reduction of Order to find the general solution to the differential equation xy" +…

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Q: Find the differential equation whose solutions correspond to the following equation. y = C1x^2 +…

A: For the solution follow the next step.

Q: Solve the Differential Equation using VARIATION OF PARAMETERS: 2y''+18y=6tan(3t)

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Q: Find the general solution of the differential equation y" – 2y – 3y = -5te-'. Use C1, C2, C3,... for…

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Q: a. y = C,e=x + Cze-2x + x

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Q: Find a particular solution of the differential equation using the method of undetermined…

A: Given : differential equation is          y''-7y'+3y=xex To find : particular solution of the…

Q: y" – 3y' + 2y = 3e + 2e2* -

A: Given,y''-3y'+2y=3ex+2e2xNow,Auxillary equation ism2-3m+2=0m2-m-2m+2=0mm-1-2m-1=0m-1m-2=0m=1,2Since…

Q: Find a general solution for the differential equation with x as the independent variable. y"' + 3y"…

A: The given differential equation,      y'''+3y''-4y'-6y=0

Q: Solve the differential equation and find the domain: xydy/dt +3x2 + y2 = 0 , y(3) = 8

A: The given differential equation should be  xydydx+3x2+y2=0 Here is the solution of the given problem…

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: On integrating, we get

Q: Find the solution to the differential equation below such that y(0) = 8 y' = 8xy – 2x - y(x) =

A: Given: y'=8xy-2x    , y(0)=8 Taking y'=8xy-2x ⇒y'-8xy=-2x To make calculation easy multiply both…

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: f''(x)=3x2integrating both side∫f''(x) dx=∫3x2 dxf'(x)=3x33+cf'(x)=x3+c ---------equation 1Now…

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: we can find the particular solution.

Q: What is the degree of the differential equation dy = 5a4 – dr3 6x2 ? |

A: Clearly the exponent of (dy/dx) is 3.

Q: y" + 4y/ + 4y = (6x – 2)e-.

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Q: Solve the differential equation using [y(0)=1} to find C 2æydx + (x² + 3y) dy =

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Q: Find the particular solution of the differential equation that satisfies the initial condition.…

A: We know, ∫f'(x) dx = f(x)+C ∫xn dx = xn+1n+1+C

Q: y = cje* + cze²r y" -y – 2y = 0 O 2y " -y' – y = 0

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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: Find the general solution of the differential equation y' + y = te-t + et and use it to determine…

A: The differential equation is given as

Q: Find the solution to the differential equation below such that y(0) = 14 y' = 10xy - 2x y(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: For which value of the constant c is the function y = 15e-® + x + c a solution of the differential…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: using initial value problem solve differential equation

Q: By the method of change of constant, y"-2y'+y = e*/x X, %3D Solve the differential equation.

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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: Verify that the differential equation is exact, and then solve it: 2ycosx + 2xe2y + (2sinx + 2x² e²y…

A: As per our bartleby guideline we are allowed to answer only 1 question at a time.Kindly please…

Q: s, p°+ 3 xp²- yp²-3xyp = 0 find the differential equation

A: Given: p3+3p2−y3p2−3y3p=0 The standard notation for p is p=dydx.

Q: Find the general solution of the differential equation, using the method of variation of parameters…

A: We will find out the required solution using variation of parameters method.

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

A: Use linear differential equation condition

Q: x (xdx + ydy) + y (xdy – ydæ) = 0

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Q: Find the particular solution that satisfles the differential equation and the initial condition.…

A: The given differential equation is  f'(x) = 8x f(0) = 9

Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: (c) Obtain the solution of the differential equation, dy dr-y = x² when x = 1 and y = 1.

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Q: Determine whether the function y = 2 sin 2x is a solution of the differential equation y′″ − 8y = 0.

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

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Q: Convert the differential equation to a Bessel equation by y = √xu, z = x³. then solve it. y" + 9x¹y…

A: Given That : the differential equation is  y"+9x4y=0y=xu To find : convert the differential equation…

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

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Q: Find the general solution of the differential equation: y' – 5y = xy. - Use lower case c for the…

A: The given differential equation is y'-5y=xy2 This can  be written as dydx-5y=xy2 Divide both the…