Find the point on the curve y = x3 – 3x for which the tangent line is parallel to the x-axis.

Q: Obtain the differential equation associated with the given function: y = Cx² + c2.

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Q: For what value of x will the curve y = x3 – 3x2 + 4 be concave upward?

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Q: Solve the Differential Equation (D² + a²)y = Tanax by the method of Variation of Parameters.

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Q: dy y3 dx x3 + xy² II

A: Given: - The differential equation is, dydx=y3x3+xy2 To show: - The given differential equation is…

Q: Find the differential equation whose solution is given by: y^2=4ax

A: To find the differential equation for y2=4ax differentiating this equation with respect to x.

Q: Solve the differential equation by variation of parameters. 4x e2x y(x) = y" - 4y =

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Q: Solve the differential equation by variation of parameters. 4x e2x y(x) = = y" - 4y =

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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: Determine whether the function y = 2 sin 2x is a solution of the differential equation y"-8y = 0.

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

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Q: Construct a linear first-order differential equation for which all solutions are asymptotic to the…

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Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-2t 2 = 0

A: We need to determine a differential equation corresponding to the general solution: y=c1e5t+c2e-2t.

Q: The tangent line to the curve y = x3 at the point (1,1) will intersect the x-axis at x = a.2/3 b.…

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Q: Find the differential equation whose general solution is y = C1x + C2ex. %3D

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Q: Find the approximate height of the curve y = x3 – 2x2 + 7 at the point where x = 2.98. (SOLVE BY…

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Q: Find a differential equation whose general solution is y = cet + c₂e-4² = 0

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Q: Find a differential equation whose general solution is y = cjet + cze-". = 0

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Q: Find the solution for the second order differential equation y-4y = x sinh x.

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

A: In this question, we need to find the value of x at which the tangent line is horizontal.

Q: Find a differential equation whose general solution is y = c₁est + c₂e-2¹. 5t = 0

A: I have given the answer in the next step. Hope you understand that

Q: Find the particular solution to the differential equation when y(0)=3 and (2)=1

A: Given differential equation isy''=y'2x-y'x2-1 The conditions are y(0)=3,  y'(2)=1

Q: Find the particular solution that satisfies the differential equation F'(X) = 10x − 12x3 with an…

A: Given the differential equation: F'x=10x-12x3 Initial condition: f3=2

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

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

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

Q: Solve the differential equation by variation of parameters. 1 y" + 3y' + 2y = 6+e* Show all your…

A: Use the procedure of method of variation of parameters to solve this problem.

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

A: Given that f'(x) = 20x3 - 8x and f(1) = 1 then find particular solution. Here i attached solution of…

Q: Use variation of parameters to solve the differential equation x²y" + 10xy' + 8y = x².

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Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-t In(t). -t 2e t²ln t…

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Q: Find a differential equation whose general solution is 9t = C₁e⁹t + c₂e-5t. y = = 0

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Q: Find all solutions to the differential equation. Use c to denote an arbitrary constant. y' = x ln(x)…

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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: Solve the differential equation. regarding y as the independent variable rather than x. by |26. (1 —…

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Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-tIn(t) y(t)

A: Given the differential equation is y''+2y'+y = e-t lnt

Q: Find the equation of the line tangent to y = x2 – 3x – 5 and parallel to the line y = 3x – 2.…

A: Explanation of the answer is as follows

Q: Solve the Differential Equation using VARIATION OF PARAMETERS: y''-2y'+1=(x+1)e2x

A: The given differential equation is: y''-2y'+y=(x+1)e2x

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

A: Given that: f'x=x3-9x2;     f2=9

Q: x" + 2x' + x = e° -t.

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Q: Find a differential equation whose general solution is y = c₁e5t + c₂e-²t. = 0

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Q: Find a differential equation whose general solution is 7t y = c₁e²t + c₂e-5t = 0

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Q: Use variation of parameters to solve the differential equation: -2x y" + 4y' + 4y : In x. = e

A: Here I am attaching image so that you understand each and every step.

Q: obtain the linear differential equation with the real, constant coefficients that is satisfied by…

A: Solution.

Q: Find the particular solution to the differential equations,Evaluate the polynimial by finding the…

A: Given that: xdy+ydx+xy(3dx+dy)=0x=-3 and y=9

Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

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Q: Find the differential equation whose solution is given by y^2=4ax

A: topic - differential equations

Q: Obtain the differential equation associated with the given function: y = Cx² + C².

A: first we will derivative with restive x then find the value of C then put in given equation

Q: Solve the differential equation using the method of undetermined coefficients. y" - 4y' = sin(3x)

A: Given differential equation is

Q: Find a differential equation whose general solution is 6t y = c₁et + c₂e -3t = 0

A: We find a differential equation whose general solution is y=c1e6t+c2e-3t.