The general solution of y" +4y" +5y'+2y 0 is (a) Ae-2* +(B+ Cx)e¯* Ae* +(B+Cx)e2* -2x (b) (c) Ae 2* +(B+ C)xe* (A+ Bx)e* +(C+ Dx)e²2r -2x (d)

Q: Evaluate L-1{ -(-e¯™s+4T8+ 2+1

A:

Q: (2x)(x-y+5)(5y)

A: Firstly, we multiply 2x by each term of x-y+5

Q: - 9x - 24 (x + 4)(x + 1) Evaluate ·S -dx + C

A:

Q: ifferentiate. 12) y = (x2 - 2x + 8) ex A) (x² + 4x + 6) ex C) (x²+6) ex 1 [ 2 ² + x + 1] x B) ex 3…

A: Given query is to find the derivative.

Q: ((x-1/4y-1)-3)/ (x5/4y0)

A:

Q: (√3-3)/6 - (√3+3) /6 12 dx 2 1+ (2x + 1)²

A:

Q: (e) 7 x² 3x2-6x x²-4x+4 (f) 1−4+1/2/2

A:

Q: (8a in simplest form.

A: 8a-3-23To write in simplest form

Q: Show the equivalent of (2x+3y) (4x² - 6xy +9y²) + (2x − 3y)(4x² + 6xy+9y²) 16x³ for x # 0.

A:

Q: 1/6a+1/4=1/2a-3/4

A: 16a+14=12a-34

Q: Find the value of each of a,b,c so that 6x3 − 7x2 − x + 2 = (x − 1)(ax2 + bx + c)

A: Given equation is : 6x3-7x2-x+2=x-1ax2+bx+c To find the value a, b, and c

Q: solve for x (x-4)2 =2x2-9x-14 If there is more than one answer, septerate with commons

A:

Q: If fx) = (1 - x)² and g(x) = 3 - x, find fg(x)) and g(fx)). fg(x)) = g(fx)) =

A:

Q: #5 Compute the equilibrium values for each of the given DDS algebraically and graphically. a) x =…

A:

Q: (c) 0$ y = cos (√√x² +1) (d) y 2x 2x +1

A: Given that: (b) y=exx2(c) y=cosx2+1(d) y=2x2x+1 The quotient rule of derivative is…

Q: If Q(x) = 7x³ + x and R(x) = 6x – 7x², find the following: %3D a) (Q – R)(x) =|| %3D b) (Q * R)(x)…

A: Given: Qx=7x3+x, Rx=6x-7x2 For finding Q-Rx,we substract Rx from Qx

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.