dy Given +1= 4x; y(–1) = 7. da The particular solution of the differential equation is a. y = 2x2 – x – 4 O b. y = 2x² – x + 4 O c. y = 2x2 + x + 4 O d. y = 2x² + x – 4 + x – 4

Q: What is the sokution of the differential equation of (2e- ry - 2y +3) de + (z*y + 2x) dy = 0? y- try…

A: Solve the Differential equation (2x^3 - xy^2 - 2y + 3)dx - (x^2y + 2x)dy = 0

Q: dy 4sin(2x) and y=2 when x=. What is the particular solution to the given differential equation? dr…

A: The given differential equation is: dydx=4sin(2x)dy=4sin(2x)dx After integrating both sides,…

Q: /9. Assume that y ==™ is a solution to the differential equation y" – 4ry – 14y = 0. Then the values…

A:

Q: 9. Use the initial condition to find the particular solution of the differential equation. y'-e =0,…

A: First we seprate the variables then integrating both sides and solve it. See 2nd step.

Q: Consider the differential equation y 3 y' - 9x 2 = 0.(a) Write it as y 3 dy = 9x 2 dx.(b) Integrate…

A:

Q: dy Given the differential equation = x2 and the initial condition y(1)= a, what is the value of a…

A: Given query is to solve the differential equation and find thw value of a.

Q: Which of the following is the particular solution of the differential equation dy dx y = 0 when x =…

A:

Q: Given that y = 3e is a solution of the differential equation %3D y" + 3y' = 0. Then, by using…

A: Follow next step

Q: The differential equation which has y = C1a + C2x as its general solution is: (a) y" 4 y' + --- 2Y =…

A: Since, you have posted multiple questions, but according to guidelines we will solve first question…

Q: determine the general solution to thegiven differential equation (D2 + 4)2(D + 1)y = 0.

A: the given differential equation is: D2+42D+1y=0

Q: a) Verify that the function y = x? + x2 is a solution of the differential equation xy' + 2y = 4x²,…

A:

Q: The auxiliary equation for the differential equation y" +3y" – 15y' = 0 is Select one: O m - 3m? +…

A: Let's find.

Q: Find the Wronskian for the differential equation dy dy 3- - 10y = 0 d.x - - dx? .A -3e30 .B 3e-3x .C…

A:

Q: For the differential equation y″+4y′+13y=0, a general solution is of the form…

A: The given differential equation is, y''+4y'+13y=0. Also, it is given that the general solution is of…

Q: Solve the differential equation. dy 3 2x – 0, y = 3 when æ = 1 dæ Using x^2 for r?. O y=x^2+x^{-3}+1…

A:

Q: The particular solution y, of the differential equation y" + 4y' + 4y = 3x? + 1 is (1/8) (1-2x+6x^2)…

A:

Q: Find the general solution of the following homogenous differential equation.…

A:

Q: Q5: Find the general solution for the following second order differential equation: y" - 4y' + 4y =…

A:

Q: Given the differential equation (y² – 2xe") dz + (2xy – z²e") dy = 0 8M ? ,What is бу | 2y – 2ey…

A:

Q: Match the differential equation with it's particular solution form. | y’’ – 6y' + 9y а. Ate 2t |y'’…

A: We have to match the following differential equation with it's particular solution form.

Q: ƏM aN 6. In the differential equation (y² –x² - 4x-1dy+2y(x+y+2)dx = 0, what is

A:

Q: dy The first order differential equation = yx +y+x + 1 is not separable. State if the statement is…

A:

Q: What is the particular solution to the differential equation 3y(x² – 1)dx + (x³ + 8y – 3x)dy = 0…

A:

Q: a) Verify that the function = x + is a solution of the differential equation xy' + 2y = 4x², (x >…

A:

Q: Verify that yp(x)=2e6x is a particular solution to the differential equation y′′ − 2y′ − 15y =18e6x…

A: Given, y''-2y-15y=18e6x Particular solution: ypx=2e6x

Q: If y(t) is the solution of the differential equation: y" - 3y' + 2y = e-2t where y'(0) = 1, y(0) =…

A: Laplace transform convert the real variables in to complex variables. The Laplace transforms of…

Q: Find the two values of k for which y(x)=ekx is a solution of the differential equation…

A: We find the two values of k for which   y(x)=ekx is a solution of the differential equation…

Q: The differential equation (y + 6xy) dx + (3y² + 12x?y) dy = 0 is O Exact with solution 32 y? 6zy5 +…

A: Differential equations

Q: Find the particular solution to the differential equation y'=3x^3 that passes through (1, 4.75),…

A: Suppose a,b be the particular solution of the differential equation. To find the particular…

Q: What is the particular solution to the differential equation x + (1+x)y = 12 with y = 0 and dy = 0…

A:

Q: Given the differential equation (D³ + 9D² + 27D+ 27) y = n(2x – 3) - . Propose an appropriate…

A: Here is the solution of the given problem. Method of Variation of parameters

Q: The particular solution that satisfies the differential equation and the initial condition dy/dx =…

A:

Q: 2. Determine whether or not y = Ce2t + C2e-4t + (1/7)e3t is a solution to the differential equation…

A: We have to check whether it is the solution of given differential equation or not.

Q: What is the general solution to the differential equation d?y + 2 dy 6x – 3 = 0 ? - dx? dx y =x² +…

A: We have to find the general solution of differential equation .

Q: Q1 (a) Find the general solution to y" + 2y' + 2y = 0. (b) Write down a linear, homogenenous 2nd…

A:

Q: The differential equation of y = Ae + Ber is: %3D o y" - 11y +24y = 0 O y" - 11y +8y 0 O y" + 11y+…

A: We have the given equation as y=Ae 3x+Be8x              ⋯⋯1 Differentiating both of the side of…

Q: b) Find the particular solution of the differential equation that satisfies the initial conditions.…

A: An initial value problem is an ordinary differential equation together with an initial condition…

Q: Let y=f(x) be a solution to y′=y^2−6y+ 5 What are the constant solutions to the differential…

A: Given that  y=f(x) be a solution to y′=y^2−6y+ 5

Q: Q2: Find the solution of the following Differential Equations 1. dx2 d²y dy – 6y = 0 - - dx 2. y" +…

A:

Q: What is the particular solution to the differential equation x + (1 + x)y = 12 with y = 0 and 2 - 0…

A: The solution is given as

Q: he auxiliary equation for the differential equation y" +2y" + 7y' = 0 is elect one: O m³ + 2m² + 7m…

A: Here we have to find auxillary equation for given differential equation as shown below

Q: Suppose that Y₁(t), Y₂(t), and Y₂(t) are solutions of the differential equation y"+5y"+(2-t)y=0.…

A:

Q: Find the general solution of the second order differential equation dy dy 3- + y = 0 dx? d.x .A Y =…

A:

Q: 2. Find the general solution to the differential equation y(4) – 7y(2) + 103y' – 4y= 0. - %3D

A: We find general solution of y(4) -7y(2)+10y'-4y=0......(1)

Q: 2x The general solution to the differential equationy"- 4y = 10e is of the form y=C₁e form of the…

A:

Q: Choose the correct answer

A:

Q: Find the general solution of the second order differential equation dy dy 10- + 24y = 0 d.x dr? .A y…

A: Given differential equation is

Q: Given that yı 1 = = 3e is a solution of the differential equation y" + 3y = 0. Then, by using…

A: Follow next step

Q: Show that the particular solution of the differential equation d²y dx² -6y-12(x+ e*) +5% dx 5 is…

A: