9) ydx+x(1+y)dy 0

Q: 7. Find. V2x dx - 1

A:

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

A:

Q: Stan5 x sec³ x dx

A:

Q: 5.[(2√x -3x)² dx

A: Given, ∫2x-3x2 dx

Q: 3 S ƒ ³√x² – 2x(x − 1) dx x2

A:

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

A: We will find out the required general solution.

Q: | 4.0°e-9* 4x³e-9a* dx

A:

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

A:

Q: 8. (D2- 2D+ 1)y = xlnx

A:

Q: 2. у -х3 -Зx? - 2 atx3D1 at x = 1

A: To find the value of this function at x=1

Q: 2-5 Secxtanx edx 4-Sečx

A:

Q: 4= Find y 13x+(2x3-x'

A: To find the derivatives

Q: 4.у%3D (2х — х3)(2х + 1)

A: Follow the procedure given below.

Q: хt — х +6 dx х3 + Зх

A: We shall use polynomial long division method to simplify our integrand.

Q: 2x+6)dx x²+2x+5

A:

Q: (xdx ydy + zdz)2z {(z²x²y²) (xdx + ydy + zdz) dz + %3D

A: Differential equation

Q: |(z + 5)(x – 7)dx Find + C

A:

Q: 5. c) [(4x³ + -)dx +

A:

Q: x3-3 5). S dx V x11

A:

Q: Find y". y = x(3x + 2)*

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.