(a) Apply first principles, to calculate the differential coefficient of (x) = 5(3x²+2) when x = 3.

Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

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Q: solve the differential equation using variation of parameters: 2x2y′′ + 5xy′ + 9y = -x2 - 2x. only…

A: The given problem is to find the solution for the given differential equation by using the variation…

Q: Determine the differential coefficient of y= V3x2 +4x -1

A:

Q: How do you test for the exactness of differential form?

A: given,      to test for the exactness of differential form

Q: Prove that the Polynomial’s Po(x) = 1 and P2(x) = 1/2 (3x²-1) are the solutions of Legendre’s…

A: The order of the differential equation is the highest derivative present in the equation. The…

Q: This is a practice question from my Differential Equations course: Show directly that the given…

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Q: Determine how the functions M(x,y) and N(x,y) can be found so that the differential equation is…

A: See the attachment

Q: Solve the differential equation: y' 2x2+y? -2xy+3y^2

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Q: Prove that the change in the dependent variable z = g´(y) transforms the equation in a linear…

A:

Q: The differential equation 3x?yy' – 3x5 = y?can be changed to linear by the substitution (a) v = y?…

A: Put y=vx So, none of these is correct option.

Q: Use an integrating factor to solve the differential equation, x²y' – 2xy = 9x² – 6

A: Given data:     The given differential equation is: x2y’-2xy=9x2-6.     The differential equation…

Q: Solve the differential g(x) = equation. g'(x) = 6x², g(0) = -6

A: The differential equation is given by g'x = 6x2 The initial condition is, g0 = -6 To evaluate: The…

Q: Form the differential equation by eliminating constants a and b from y = a(b – z)(b+1) + 52. %3D

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: How do I solve this differential equation using P(x), Q(x) and v(x)?

A: The given differential equation is,

Q: f(x) = 2x + 1; ¹/f = x² d.x

A: Solution: Given, f(x) = 2x + 1;  dfdx=x2 We have to check whether f(x) = 2x+1 is the solution to the…

Q: The proportion of people in a community infected with a virus that stays active for two weeks is x…

A: The complete solutions are given below

Q: Find the linear differential equation that is satisfied by y=xe-xsin3x+2e-xcos3x.

A: Let's find linear differential equation.

Q: Find the differential equation such that y(x) = c₁(x-4) 8 +c₂ln(x-4) (x-4) 8

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Q: The differential operator (D- 7)* annihilates the functions

A: We have to solve the problem:

Q: -3z y" + 6y' + 9y = for a> 0.

A:

Q: what is the differential coefficient of x.

A: To find differential coefficient of x we need to differentiate x with respect to x.