Write down the general solution of 4x? – 2xy + 2+ (4y – x² + 2)y' = 0, x > 0, y > 0 You should express the solution implicitly, equating the polynomial expression to the arbitrary constant c (do not use capital c).

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

A:

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

A:

Q: Use the method of undetermined coefficients to solve the differential equa- -2x y" + 5y' + 6y = e-®…

A:

Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &…

Q: If y = x2 – 2x and x changes from 2 to 2.01, find ∆y. (SOLVE BY USING DIFFERENTIAL EQUATIONS)

A:

Q: Determine whether the function y = x3 is a solution of the differential equation 2xy′ + 4y = 10x3 .

A:

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 the general solution of the differential equation xdy+ydx=2x^2ydx

A: Given differential equation is xdy+ydx=2x2ydx. We have to find the general solution of the given…

Q: Solve the differential equation 5y" - 5x?y" -10xy' + 100y = 0. Then evaluate the Legendre polynomial…

A: The given problem is to solve the given differential equation and to evaluate legendre polynomial at…

Q: Find the general solution for y''=2t+3 by direct integration and by the method of undetermied…

A: Given that      y" = 2t + 3 Here we have to find the general solution by direct integration and by…

Q: Determine (4x³ + 3x2 + 5) from the first principle when x = 2 Determine the differential coefficient…

A:

Q: Determine whether y = 2x is a solution of the differential equation y'= 6x², a. 6x2- and by'= 6r?…

A: Just take derivative of y and substitute in given differential equation and see if it satisfies the…

Q: 5. Use the properties of differential operators to solve for the product of (D+x²)(xD + 2)y

A: Given: D+x2xD+2y To find: Solution

Q: Solve the differential equation. f'(x) = 10x – 12.3 f(3) = 2 -

A: Given query is to find the solution of the differential equation.

Q: y" + 25y = 0, y(0) = 4.6, y'(0) = -1.2

A:

Q: Solve the differential equaton 2x2dy=(x+y)2dx

A:

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: 2. (x +1)y'+y = x² – 1 %3D -

A: Topic = Differential equation

Q: Find a differential equation whose general solution is 8t -6t y = cje + c2e = 0

A:

Q: Determine the differential coefficient of y = √(3x2 + 4x - 1)

A:

Q: Find the differential equation whose general solution is y = c1 x + c2 e

A:

Q: The differential equation ax - x-2y+3 2x+3y-4 is reduced to [homogenous or separable

A:

Q: Solve the differential equation 5y" - 5x²y" -10xy' + 100y = 0 . Then evaluate the Legendre…

A:

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

A:

Q: Solve the differential Egueations Zydx - (3xy*dx- xdy =0 When

A:

Q: 4. f'(x) = 10x - 12x', f(3) = 2

A: Find the particular solution of the following equation f'(x) = 10x - 12x^3, with f(3)=2

Q: Find a differential equation whose general solution is 9t y = c₁e⁹t + c₂e-²t = 0

A:

Q: b).Solve the differential equation - 2 – 3y = 4x – 5 + 6xe²x by method of undetermir coefficients.

A:

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

A: we can find the particular solution.

Q: use some form of technology to factorthe auxiliary polynomial of the given differential…

A: We can use Linear Algebra Capabilities of Maple to achieve the factoring as follows:   The auxiliary…

Q: Solve the differential equation by using variable separable method: (1+x²)xy = (1+y²)(1 +x² + x) %3D

A: We have to solve the given differential equation by using the variable separable method…

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: We have given the general solution y = C1 + C2e2xcos 5x +  C3e2xsin 5x

Q: Solve the differential equation 5y" - 5x2y" -10xy' + 100y = 0 . Then evaluate the Legendre…

A:

Q: Solve the differential equation by using variation parameter method y''-6y'+9y=8+e^-9x

A:

Q: Solve (D² – 1) y =(x³ +2x² +x +6)e²* using differential operators method.

A: Differential equation.

Q: Q2// FIND THE GENERAL SOLUTION WHEN THE DIFFERENTIAL EQUAION IS ỳ + 3ỳ + 2y = 36xe*

A: Given differential equation is y"+3y'+2y=36xex

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

A:

Q: solve the differential equation for p x + 2(xp-y) + p^2 = 0

A:

Q: What are the roots of the characteristic polynomial for the differential equation y" + 4y' – 5y = 0?

A: Given differential equation:-   y" + 4y' -5y = 0

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

A: using initial value problem solve differential equation

Q: Solve the differential equa 5. y' = 2x?y – 4y %3D

A: The solution for the asked question is given as

Q: General solutions for Legendre differential equations (2x + 3)2 + (2x + 3) + y = 0 is....

A:

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

A:

Q: Q9// FIND THE GENERAL SOLUTION WHEN THE DIFFERENTIAL EQUAION IS ỳ +ỳ – 6y = 4

A:

Q: Solve the differential equation 5y" - 5x²y" -10xy' + 100y = 0 . Then evaluate the Legendre…

A:

Q: Solve the differential equation by variable separable method dy (1+ y) (3x² + 6) = 2- dr 13 + 6z

A: To find- Solve the differential equation by variable separable method dydx = 21 + y23x2 + 6x3 + 6x

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 6t y = c₁et + c₂e -3t = 0

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

Q: (D² – 2D + 5) y = 25x² + 12

A: Given: D2-2D+5y=25x2+12 So,  The auxiliary equation is: m2-2m+5=0 Now solve; m2-2m+5=0m1,…