Find y subject to the conditions y'(6) = 88, y(6) = 90. %3D 2.r2-3r, %3D y" (Caution: Once you move forward you cannot go back to a question) + 2x + 6 + 2z + 6 2 +2z +6 2x-6 2 2x - 6 2 6.

Q: {3x+y=-3 2x+3y=5 (X,y) =

A: Given: 3x+y=-32x+3y=5 To Find: The value of x,y.

Q: 1. (D2 + 2D + 4)y = 8x? + 12e-*

A:

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

A: We will find out the required general solution.

Q: 2(a + 3x) = y - 4x for y

A: Given query is to solve for y.

Q: 4t 3. -2

A:

Q: d Differentiate (-16x-1 +4x + 2) when x dx

A:

Q: 2 X 2.- (D*- 4D +4)y = x *

A:

Q: 6y²dx- x(2x³ +y)dy = 0 a. x³yi = y#+ c b. x-3yi 2y+ c C. x³yi= yi+ c -y= 2y+ c d. x

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: -x+y+3z = 3 x+2y-z 0 3x+2y %3D -5z = -2

A:

Q: Dª + 4D³ – 3D² − 2D + 1)y = 0

A:

Q: (5, 2)

A:

Q: (D²-2D-3)y=64xe³x

A: We have to solve the given differential equation.

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

A: We can find the integration as below.

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

A:

Q: 1 x+1 ST (2y-2)dydx Evaluate 0 °0

A:

Q: How do I differentiate this?

A: am*n=(am)n

Q: Find the point on the line 2x + y = 7 that is closest to the point (−4, 2).

A: We use second derivative test to find out point where distance minimum

Q: 2. (D² + 3D + 2)y= 1+ 3x + x²

A:

Q: 2 D²y+y=secx²

A:

Q: 6. sec²(3x) – V8 W%3= 6x +9 0.

A:

Q: 2x-3y=1 -6x+9y=-3

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: If x = 3 and y = 7, then 1/x + 1/y

A: We have to find

Q: у %3D 5х 2 — 2х + 3 =

A: Giveny=5x-2-2x+3  Formulae for derivativedydx(xn)=nxn-1 where n is integer and x is variabledydx(c)…

Q: (3x2 + бху?) dx + (бх?у + 4у) dy %3D0

A: Given differential equations is an exact equation

Q: (D² + 6D + 7)(D3 – 5D² + 6D)y = %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.