: Write step by step solutions and justify your answers. 1).- ! Solve the following Initial Value Problem: y" – 25y = 0, y(0) = 3 and y'(0) = 0. %3D 2).. -] Solve the following Initial Value Problem: y" + 3y - 18y = 0, y(0) = 1 y (0) = -1. %3D %3D %3D

Q: (a)((x+1)² – y²)ª– (2(x+1)y – 10(x+1)²) = 0 dx

A:

Q: 3.) (2xy³ + y4)dx - (2y - y³x)dy=0

A:

Q: FIND THE GENERAL EQUATION OF THE FOLLOWING SOLUTION: y" = 12 %3D A.

A: A) The differential equation is given as y''' = 12 On integrating both sides , we get ∫y''' = ∫12y''…

Q: . Solve by using variation of parameters: y" – 10y' + 16y = 4e*

A: We have to solve the differential  equation  using variation of parameter.

Q: Solve y(6) — 5y(4) + 16y" +36y" - 16y' - 32y = 0. Include a plot of the solution curves.

A: There is no conditions, so i plot the six independent functions separately.

Q: y" + 4y = 28/4 y(0) = 1/2, y'(0) = 0

A: Let Y(s) be the laplace transform of…

Q: Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0 %3D

A: 2x+62y2+3dx+4yx2+3x+2dy=0

Q: Find the general solution of the given equation y" + y = 0

A:

Q: (ii) 4x²y" + y = 0.

A: Solution

Q: X = y + % y = 0.000396707 – 0.24576 x2 22 = 0.00029753 - 0.12288 x²

A:

Q: Solve csc(x) – 2 = 0 on [0, 27]

A: Let's find.

Q: Find all solutions to the equation: csc²(x) - 6cot(x) = -4.

A:

Q: Q1. Solve the following first order equations: (b) (e* + y)dx + (2+ z + ye")dy = 0, y(0) = 1. %3D…

A: EXACT DIFFERENTIAL EQUATION,

Q: -zy=0

A: Topic- Differential Equation

Q: Example 12: Solve: (y - 2xy)dx= (x² – 2xy)dy %3D

A: Given that :  A defferential equation is given.  Now solve it

Q: 1. Solve the equation y2 + 6x = y(3y – 2x)y'

A:

Q: mistake

A:

Q: Solve by undetermined coefficients. y" – 3y' = 6e – 2e", y(0) = 0, y (0) = 0.

A:

Q: (а) Consider the following equation: xy dy – (3x² + 4y²) dx = 0 | (1) State the order of the…

A: Questions from differential equations.

Q: (ii) 42?у" + у — 0. 4.x

A: Consider x=et and differentiate to obtain the expression of dtdx . x=ett=lnxdtdx=d dxlnx=1x Break…

Q: Solve y"-2y"-5y'+6y=0 general solution y(x) =

A: solution of the given problem is below...

Q: y(5)_y(3) = e²+2x²-5 y(4) + 5y" + 4y = sinx + cos2x

A: Given: The equations are y5-y3=e2+2x2-5 and y4+5y''+4y=sin x+ cos 2x. The objective is to find the…

Q: Find the particular solution of each of the following. 1. (2х - 3у +2)dx - (Зх + 4у-5); у(-3) %3D 4

A: We know that M(x, y) dx+N(x, y) dy=0……(1) is a differential equation. Equation (1) is exact if and…

Q: Solve the IVP by substitution. (3x2 - 2y2)y' = 2xy;  y(0) = -1

A: Substitute  x = vy and than solve using method of separation of variables.

Q: form.

A: The given differential equation is not exact .And the solution is:

Q: 4 Solve for y(x) y"-y-16=0

A:

Q: dy Solve = dx 2-y 2-x

A: To solve the given differential equation

Q: A' C 2. B C' B'X 0 2 4 6 ? . 8.

A:

Q: Solve step by step in digital format 4.-(4- y²) dx - (4x²)dy = 0 Solve step by step in digital…

A:

Q: S" (2x + 1)ea(x+x)dx, b > 0, a is a constant

A: