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: Find the general solution to the equation xdx + -dy= 3dy O x=/2y+ Cy-2 O xy= 2y + C O y = 2x3 + C…

A:

Q: 4. A sketch of r(x) is shown. Which of the following could be an equation for r(x)? a. r(x) = (x-a)…

A: The given graph of r(x) has zeros at point a , -b and  -c . For the zeros of r(x) , put  r(x)=0 .…

Q: y′ = 2y − 3

A: Given,

Q: find the components of −→P Q. P = (1, −4), Q = (3, 5)

A: Given two points P(x1,y1) and Q (x2,y2) their difference                   PQ → =…

Q: 2² - 8x + y – 10y - 44 = 0

A: topic - circles

Q: Let fi (2) = - 5x – 5, f2(x) = – 6x² – 8x – 3, f3(x) = 2a² + 10x + 3, and fa(x) = 2x – 9. Find a…

A:

Q: Find S(-3e-3t + Vt)dt

A: Basic integration formulas are used. I have stated the used formulas in the solution.

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: 2 2 4x – 9y = 1 find the thirdderivative

A: Given that 4x2-9y2=1 Find the third derivative

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

A:

Q: (a) Show that y-C, + C2 2* – k is a solution of ya+2- 3yk+1 + 2y% %3D

A: Given difference equation, yk+2-3yk+1+2yk=1 To show that yk=C1+C22k-k is a solution of above…

Q: 3. Find the general solutions of, (xy + x* )dy + y°dx = 0 b.

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: 2. x + y – z = 2   2x + 2y - 2z = ­6  5x + y – 3z = 8

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

A:

Q: y²dx+x(x+y) dy=0 A xy² = c(x+2y) x²y=c(x+2y) xy² = c(2xy) x+y²=c(2xy) B C D

A: Given: The equation is y2dx+x(x+y)dy=0. To find: The correct option for the solution of the given…

Q: Find β such that the equation βx 2 + x + β = 0 has a repeated real solution.

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: 4. Obtain the general solution (D³ + D² - 9D - Dly = 6e*+ 3° 3x 3xe

A:

Q: 6 - Show that x(t) = (C1 + C2t) e¬t is a valid solution to i + 2yi + 7²x = 0.

A:

Q: Find the linearization at x = a. y = (10 + x)-1/2, a = 9 (Use symbolic notation and fractions where…

A:

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: What is the sum of 7x*+2xy-5y and 2x+3xy+2y7 14x +6x3y2-10y 14x +6xy-10y 9x8+5x3y2-3y 9x*+5xy-3y3

A:

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

A:

Q: Find the general solution of the equation ¤(x – 1)y" – (2x – 1)y' + 2y = 0 by the reducing the…

A:

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.