y = c1e3x + c2e−x − 2x  is a two-parameter family of the second-order DE  y″ − 2y′ − 3y = 6x + 4. Find  c1  and  c2  given the following initial conditions. (Your answers will not contain a variable.) y(−1) = 0,    y′(−1) = 1

Q: y(4) + 18y" + 81y = 0

A:

Q: Find the solution. (D-3D-2)y = 0 when x 0, y = 0 and y' 9, y" = 0 a. y = 2e- (3x-2)e* b. y 2ex+…

A:

Q: What are the zeros of P(x) = (x - 3)(x + 1) (x – 1)? %3D

A:

Q: Find particular Solution of y-2y'ty =x-6x +2xe a 2.

A: Solution.  Given the differential equation                   y''-2y'+y=x2-6x+2x2 ex…

Q: wouldn't there be a t in the second term of the general solution?

A:

Q: Solve the following linear differential equation system, i.e., find y₂(t). dyn (1) dt dyż (t) dt =…

A:

Q: yl=8sin4x, y(0)=6 Select the correct response: O y=2cos4x+8 O y=-2cos4x+8 y=-2cos4x+6

A:

Q: Evalutate: limx→5 O-2 04 05 x-5 √x-1-2

A:

Q: Determine which of the following equations have integer solutions (x, y) = Z²: 1. 465x +4920y 1 2.…

A: Introduction: The linear Diophantine equation of the form ax+by=c has integer solution if and only…

Q: Find all solutions of x2 - x + 2 = 0 over Z3[i].

A: To solve this equation in Z3[i], we need to find all complex numbers of the form a + bi where a and…

Q: Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y + 3x) dy B.…

A: we need to find out at which of the equations has solution of the form F(x,y)=c

Q: Find a particular solution to

A:

Q: 3. Show that y = 5x2 +2 is a solution to the DE ry' +y" = 2y.

A:

Q: Verify that x = C1et + C2 is a solution to x′′ − x′ = 0.

A: To Verify that x = C1et + C2 is a solution to x′′ − x′ = 0.

Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

A:

Q: find the general salution of ly-3y12)de = xdy,

A:

Q: /| (9x + y – 2z) dS. Is Evaluate S: z = x + 0 < x< 4, 0 <y< 7

A: Given: ∫∫S9x+y-2zdSS:z=x+y2, 0≤x≤4, 0≤y≤7

Q: 2. If x =-1 and z = 2y = -3x, find the value of 3xy-z 1+3x²z

A:

Q: 2. Show that x4 - 3x - 1 has a solution between 1 and 0, and another solution between 1 and 2.

A:

Q: Find the general solution of the fifth-order DEQ. 2x(5) – 7x(4) + 12x" + 8x" = 0

A:

Q: Is  (6, 2)(6, 2) a solution of  x−5y=−3x−5y=−3?

A: Consider the given equation for x and y:

Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: 1 2 1 | | (x² + y»2 + z²)dzdydx lo Jo

A: To evaluate the given triple integral: ∫-10∫02∫01(x2+y2+z2) dz dy dx=∫-10∫02∫01(x2+y2+z2) dz dy…

Q: Solve the following DE: (1+ y² + xy²) dx + (x²y + y + 2xy) dy=0 O2y²+x²(1+x)²=C O 2y²+x²(y + x)² =c…

A:

Q: If x/4 = y/3 = z/2, then what would be the value of (5x + y – 2z) / 3y

A: To find: The value of 5x+y-2z3y. Given: The equation is x4=y3=z2. Calculation: Assume x4=y3=z2 is k,…

Q: 2 =[41] −1 4 If A = find (AT)-¹.

A:

Q: Which of the following equations has a solution of the form F(x,y) = C 3x) dx = 0 dx A. 2x + 3y +…

A: To determine which of the following equations has a solution of the form F(x, y)=C.A…

Q: Which is a correct solution of y = 4x – 3? O (1, 3) O (1, 2) O (0, 1) O (2, 5)

A: The given equation is y=4x-3

Q: x + 3y − z = 2 x + y − z = 0  3x + 2y − 3z = −1

A:

Q: (17) Find the solution of the following second-order difference equation: an+2 – 4an+1+ 8an = 0, ao…

A: Difference equation we can easily solve using auxiliary equation.

Q: 7. Find the solution of the differential equation (D' + 5D + 6)y = 0 + Cze* D. y = C;e-3x + Cze-* A.…

A: Given that differential equation  we have to find the solution of  that differential equation

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.