The function y(x) = x³ – is a solution of which of the following initial value problems? (a) ry' + 3y = 6r³, y(1) = 0 (b) xy' + 3y = 0, y(1) = 0 (c) ry +3y = 6x-³, y(1) = 0 (d) ry' + 3y = 0, y(0) = 0.

Q: Q3/ Solve the following equations: 1- х(2у — 3)dx + (x2 + 1)dy %3D0 dy 2- dx 4y x (у-3) 3. y' = 2xy…

A: Note that there are so many ways to write the final answer of the differential equation.

Q: The values of C, and C₂ so that y(x) = C₁x + C₂ (-) satisfies the two conditions y(1) = 1 and y'(1)…

A: Given: yx=C1x+C2-13x2 To find the values of C1 and C2 such that y1=1 and y'1=-1.

Q: Solve for y(x):  y’’ – 5y’ + 12y = 0; y(2) = 0; y’(2) = -4

A:

Q: Q2\ Solve the following 2y +3y'- 2y = te-2t y(0)=0 and y'(0)=2 %3D |

A:

Q: Determine (without solving the problem) an interval in which the solution of (9-1²)y + 2ty = 4t²,…

A:

Q: Solve: y' + 7y +9y' +9y=0 y(x)

A:

Q: y" + 7y' + 10y = -1lte".

A:

Q: G(y) = (y − 1)4 / (y2 + 2y)7 Find G'(y) =

A: for a polynomial function of power n: Division rule of differentiation:         Chain rule :…

Q: 5. Solve 2y" - 3y' - 2y = 0; y(0) = 1, y'(0) = -1.

A:

Q: Given y'' + 2y' + y = 3te-t when t = 0 and x = 4 and x' = 2. Solve for its solution Y (s). a. Y(s)…

A: Here we use the Laplace transform under differential equation, and use shifting property of laplace…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.