Solve the equa^n, x(d²y/dx²)+(dy/dx)+xy=0 in series || (#ForbeniousMethodCase-2)

This is a video of Forbenious Method Case-2 of Solution in Series chapter part-4,

part-3
Solve 4x(d²y/dx²)+3(dy/dx)+3y=0 near the origin

part-2,
Solve (d²y/dx²)-2x²(dy/dx)+4xy=x²+2x+2 in power of x

Part -1,
solve the equation (1-x²)(d²y/dx²)-6x(dy/dx)-4y=0 in Series near the ordinary point X=0

Method of variation parameters part-5

#{(d³y/dx³)-6(d²y/dx²)+11(dy/dx)-6y=e^2x}

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part-4
#{x²(d²y/dx²)-x(dy/dx)-3y=x²logx}

part -3
#{(d²y/dx²)+3(dy/dx)+2y=e^(e^x)}

part-2
#{(D²-2D+1)=e^2x/(e^x+1)²}

part -1
(d²y/dx²)-3(dy/dx)+2y=e^x/(1+e^x)

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All Questions paper playlist:---------

Differential equations playlist:---------

Partial Differential equation playlist:-------

Complex Analysis playlist:---------

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

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