2 y' = -x - 2 y – x + 7 1 y A) (y – x)³ + 14y2 + 4x² = 9 B) (y – x)² – 14y +x + 9 = 0 C) (y – x)² + 14y + 4x = 9 II

Q: 3) V12-b+4= 6

A: #3 Given,   12-b+4=6

Q: = f(2y + 3)²√√y+2 dy

A: To solve the given integral

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

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

Q: (11) Evaluate [[3x+5y+i(x²-y') dz along y=x (0,0)

A:

Q: x2 + 2y2 + 3z2 = 1

A:

Q: (a1x + bịy + c1)dx + (a2x + b2y + c2)dy = 0

A: We will find out the required general solution.

Q: 1. Find 2(3z + 4)² dz.

A:

Q: D2 – 5D +6)y=3xex+2x2 , y(0)=0,y,(0)=1

A: Given differential equation is homogeneous ordinary differential equation. To solve this equation…

Q: SG3" + y2n + y")(2y2" + 3 y" + 6) dy. ,311

A: Explained below

Q: d (3y? + 4y +2 Find dy y

A:

Q: Differentiate y = 21/2 4 - x (4 – x³)'"2 -

A:

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: 6xy — 2x — 8zx2 = 0 6xy — у — 2zy2 = 0 4x² + y² − 2 = 0

A:

Q: (х? + 2у — 10у3х) if z у? (у? + 4х + 5у) dz -, find || дх

A: Given:

Q: If (4x + xy):(5xy - y*) = 12:5, find x: y

A:

Q: Given g(x) = 6x – 15x +4x +8x–4 and )= 3x² – 3x – 1, what is the quotient ? A 2x – 17x+10 A 2x-5 B.…

A:

Q: ду Find ду and when dz (a) y = 6 + 3x + 16z + 4x2 + 2z2 (b) y = 14x2 (c) y = 9 + 4xz - 3x2 %3D

A:

Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: 9x-y+z=3 10x-y+z=8 Find (x,y,z)

A:

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: 2. (D³ – D)y = -2(1+x) + 4e* – 6e¬× + 96e3x

A:

Q: 3. y = (x+b)(x-a). (x-b) ; y

A: A detailed solution is given below. Use logarithmic differential to solve it.

Q: 6. (t -1)+(2 8. (2x² +5xy+ 3y²)+(8x² –7y²)

A: 6.

Q: 1 4. (1+2)y/ + 2ry = (1+2)y

A:

Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

Q: 3y +5 (5y-7)2 dy

A: We can find the integration as below.

Q: 1. Given the algebraic function x² xy + y² = 3

A:

Q: y(4) + 3y" - 4y = 0

A:

Q: (y + 4)(y² + 8y}Vy² + 8y – 1 dy

A:

Q: 7x-4y-3z = 21 -4x+7y-z = 0 -3x-y+5z = 0 x, y, z?

A: Given

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.