نقطتان )2( What is the Form of the General * ?Solution for this equation A. y(x) = Aemx + Bemx dy? dy + dx? - 6y 0 B. y(x) = (A + Bx)emx %3D dx C. y(x) = e"*(c cos ßx + D sin Bx)

Q: (5-)dx ー3 2人 がー。 Sin(x) d X

A: 3)   ∫-34(5-x2) dx=5x-x24-34                                =54+3-16-94…

Q: sin x dx 4 3 Show that -

A: The integration can be written as;

Q: (sinx)" dx is:- 4) The solution of (sin x) dx A) (sinx)' dx B) C) Zero

A: ∫0πsinx7dx=∫0πsin7xdxWe know…

Q: 1. у%3D х3 — 2x2 + 3х — 5 y = 3 — 2х2 + 3х — 5 dy — Зx2 — 4х + 3 dx

A: Given: y=x3-2x2+3x-5

Q: 6. (a) cos 2x dx; u = 2x

A:

Q: y + (cos x) y =3 sinx.cosx

A:

Q: x – sin 2x -dx x + cos2x

A:

Q: 3- cos nX Sin ux dx

A:

Q: 6e(6 sin 3x) dx sec 3x

A: Inverse of sec3x is cos3x Cos3x=(1/Sec3x) Putting in the integration problem

Q: y-e" sec! x-3x° 2 csC X Sin x-2X

A: on doing the differentiation of this we get the

Q: 4 fcos 3x sin³ 3x dx

A:

Q: (х + 7)/3 — х dx

A:

Q: sketch the graph of the function Qu, y= 3 sin tx -1

A: Given function is  y= 3sin(x/2)-1

Q: 2. dx 2. Solue integra

A:

Q: dx Evaluate V- x² – 4x – 1

A:

Q: 1. x2 cos 2x dx

A: The given integral is: ∫x2cos 2x dx

Q: on(1-y)csc²( y) dy

A: This question can be solved using the concept of integration by substitution.

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.