Solve the given initial value problem. 6x y+ y? dy y (3) = -2 dx 216 + 3xy O x +xy = 948 O - xy = 2940 xy? -y = 964 O +xy = 2892 O y? +y = 2908

Q: x-2X x+ X-6

A: Here we have to calculate the givne limit.  =limx→2x2-2xx2+x-6

Q: Solve for y: x/4 + y/9 = 1

A:

Q: Evaluate. [(122 - 9x 2) dx S(122 - 9x +2) . (Use C as the arbitrary constant.) dx =

A:

Q: 5 = 2 / 3 x + y. solve for x in terms of y.

A:

Q: x² – 2x dx

A: Given integral can be written as By using the following substitution we get

Q: 2 X 1 dx -2 4

A: Let's see a formula of integration. ∫a2-x2 dx = x2a2-x2 + a22sin-1xa + C We use this formula to…

Q: 14 x= F X D 5 E 12 B A

A:

Q: Solve (2y +5)dx = 6dy O a. y = 3In(2x+5)+ c O b. x = 3In(2y +5)+c x =- In(2y+5) +c O d. x =…

A: Given that          (2y + 5)dx = 6dy Now we solve this differential equation.

Q: A 1 x る8 %3D 은 AB=C Find X+g?

A:

Q: y=2.2x+12      x= y=2x−6.1     x= y=5(x+5)−1 x=

A: 1. Given y = 2.2x + 12 y= 4x + 12 4x = y - 12 x = (y - 12)/4 Or   x = (y/4) - 3

Q: xx5+G dx 4.

A: To find the integral , using a suitable substitution

Q: %3| Find the value of k if the f(kx2 – 2x + 3)dx = 14.

A: Definite integration

Q: (4x+2x)e dx

A:

Q: = 4 y = 2x – 1 :-y

A: Topic - linear equation In two Variables

Q: Solve for x. * (7x) (7x) I (4x) (4x)) F (7x) (7x)/ H. O x= 36 O x= 20 O x= 10 O x = 24

A: the sum of the interior angles of a hexagon is 720 degrees.

Q: (² X x2 + 4x + 13 dx

A:

Q: r4 3 +1 d y? 1

A: We will solve the problem

Q: Solve for the general solution (D4 – 16)y = x* + x + 1

A:

Q: 1 e2x + 5ех 4 e2x + 4ex

A: Given: ∫ 14e2x+5exe2x+4ex dx= 14∫ ex+20ex+4 dx    (Multiply and divided by e-x)

Q: Solve for for the equation y = aln(x + )+ 4tan(;)– 2x O a. T O b. In(4 + x) O c. none of these O d.…

A:

Q: S,(2x-y)dxdydz

A: Consider the integral: ∫12∫0z2∫0y-z2x-ydxdydz

Q: 2 d'y If y = 3x 4 4x + 18x find 2 dx

A:

Q: Solve for y.   5/2y - 7/3y = 1

A:

Q: Solve for y X2 =9e?y

A: Given: x2=9e2y As we know that the exponent rule: lnm=x⇔m=ex So, we can also write as:…

Q: 3. S tan¯¹ √√x dx

A:

Q: solve for y. 3y = 2y+1

A: 3y=2y+1

Q: Evaluate. 25х —31 dx J (x + 5)(x² + 1) %3D

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.