Solve the equ^n || (dy/dx)²-y(d²y/dx²)=n{(dy/dx)²+a²(d²y/dx²)²}^1/2 || exact diff equ^n & some spe..

This is a video of exact differential equation & some special form chepter , part-2

burdwan University

2nd sem

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challenge 1.------------------------
Solve, cos(x+y)p+sin(x+y)q=(z+1/z)

challenge 2.------------------------
Solve, (xy³-2x⁴)p+(2y⁴-x³y)q=9z(x³-y³)

challenge 3.-------------------------
Solve, x(du/dx)+y(du/dy)+z(du/dz)=ku+(xy/z)

challenge 4.-------------------------
Solve, z(z²+xy)(px-qy)=x⁴

(group theory):-------------------------
Let G be a group of order 35 (or133) .Show that G is cyclic.

(Find the Radius of convergence part 1):-------------

Cauchy's integral formula part 5:------------------

Exact differential equation & some special form part 4
(d³y/dx³)=2(d²y/dx²)(dy/dx)

Find Yc & Yp ??
(d⁴y/dx⁴)-y=xsinx

Homogeneous linear equations with variable coefficient:---------
part 1
x²(d²y/dx²)+4x(dy/dx)+2y =e^x

part 2
x²(d²y/dx²)+x(dy/dx)-y=x²e^2x

part 4
(x⁴D⁴+2x³D³+x²D²-xD+1)y=logx

Singular solution:--------------

part-1
4p²x(x-a)(x-b)={3x²-2x(a+b)+ab}²

part-2
p²y²cos²(alpha)-2pxysin²(alpha)+y²-x²sin²(alpha)

Method of undetermined coefficient:---------

part-1
(d²y/dx²)-3(dy/dx)=(x+e^xsinx)

part-2
(d²y/dx²)-7(dy/dx)+6y=(x-2)e^x