11. What is the general solution of (2a-y)dx + (4x +y-6)dy 0 (a + y- 3) = c(2a+y-4)2 (x - y + 3) = c(2a +y-4) O Option 1 Option 2 (a- y- 3) = c(2r -y-4) (a+y-3) = c(x+ 2y- 4)

Q: Which statement about the linear equation 3a + 1/3 * (6a - 9) = 1/2 * (10a - 6) is true?

A:

Q: J(x-3x)dx = x' 3x +C 2 -3х + С 4 b. 3x-3+C 3x+C 4 4x* -6x +C

A:

Q: 3y3 (2y+3) (y-5)

A: The given expression is

Q: xp | %3D P O O d. dy -43xcsc(5x)[5cot(5x)– 3ln(4)] xp -43Xcsc(5x)[5cot(5x)+ 3In(4)] Oc. dy %3D xp |…

A: We have to find

Q: x1 J: (x2+2x)2 dx= (x2+2x)3 C (x2 2x)3 C + 3 (x2+2x)3 +C 6 22-1C + -2 2x)1+C

A:

Q: (5 + y)(4 + y) = (6x + 2y – 4) + (2x + 2y + 10) = (x – 3)(x + 3) =

A:

Q: The general solution of (D³-5D2-6D)y=0 is Ay=c₁+c₂e2x + c3e³ B) y=c₁+c₂e-2x + c3e-3x y=c₁ex+c₂e²x +…

A:

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

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

Q: Without using the fact that the complement of an open set is a closed set, prove that if SCR such…

A:

Q: x2 + 2y2 + 3z2 = 1

A:

Q: Suppose x² y² = x + 17y x = y Find 17 x + y x² + y² + 1

A: Given that, x2=17x+y, y2=x+17y, x≠y Find the value of x2+y2+1. As we know the formula: a2-b2=a-ba+b

Q: (x²-x) y¹ = (x²+1) y + 12x (x²-1) ³ y' when x = 2, Y = 9

A: Given differential equation is  x3-x y' = x2+1 y  + 12 x x2-13                      ⇒      x3-x…

Q: The general solution of (D-4D)y-0 is (A y=c+ cx + Cze tk ® y-(c, + cx)e* +c3e* © y-c+ cx +Cye" -4x D…

A:

Q: 35. Solve this auxiliary DE y"" – y" – 4y = 0,when x = 4, y = 0

A:

Q: Solve (x²y + y³) dx 5(1+x²y-²) 18 18(1-y²x-2) 5 a. b. C. d. X Y X y = 18(1-x²y-2) 5 5(1+y²x-²) 18…

A:

Q: 2-5 Secxtanx edx 4-Sečx

A:

Q: If  x3 + y3 = 30, x+y =6, then 1/x+1/y = ?

A: We need to find,

Q: 7. x = y + 2z - w = -1 2x + y2z - 2w = -2 -x + 2y4z + w = 1 3x - 3w = -3

A:

Q: (x + y + z)(3x - 2y - z)

A: we have to solve: (x + y + z)(3x - 2y - z)

Q: Find a, b, c, d for P(x) : = ax3 + bx? + cx + d if P(1) = 11, b = 3d, a = 2c and P(x) = Q(x) + x+1'

A: Polynomial and remainder

Q: (3) J -x² + 4x 2 x³ + 4x² + 4x + 3 dx

A:

Q: sx2-9x-6 dx x3-2x2- 4xt8

A:

Q: solve (2x+1)(x-1)=(y+5)(2y-5)

A: First we use distributive property on both sides. And then we move all the terms of the right side…

Q: 3(y+7)-7y=1 y=

A: First we distribute 3.

Q: 2. loq, (5xf4)=3

A: To find the value of the x.

Q: 2 x²+yi -I -VI-2²

A:

Q: (x3-4) 2. S dx x3+2x2+2x

A: To evalaute: I=∫x3-4x3+2x2+2xdx=∫1-2x2+2x+4x3+2x2+2xdx=∫dx-∫2x2+2x+4x3+2x2+2xdx

Q: 2x + y = 23 and x + 2y = 17, then 3x - 3y = ?

A:

Q: x4 + 3x2 + 4 dx (x + 1)²

A: Consider the given: ∫ x4+3x2+4x+12dxOn division: x4+3x2+4x+12=x2−2x+6+−10x−2x2+2x+1∫…

Q: 9) (4y? + 10xy – 4y + 8)dx + (2x² + 2xy – x)dy = 0 ; when y(0) = 1 %3D

A:

Q: S (3×412メ -15)2 2dx

A: The integral is solved as follows :

Q: (d) (* + y, x - v)

A: We have given a vector field (x+y,x-y) with four diagrams;

Q: 1) 2x+8y=20 y=2

A: 2x+8y=20..................1y=2.............................2

Q: 2. Show that (2x + i)(2x– i) = 4x +1 %3D |

A: Prove the 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.