Example 2.3 Find the complete solution of the following second-order ordinary differential equation x + 6x + 9x = 0

Q: y' + p(x)y = q(x), p(x), q(x) E C(I)

A: We have to find the general solution of differenrial equation

Q: y(1 − lny) d² + (1 + lny) ª dx² dx² = 0

A: Differential equation y1-lnyd2ydx2+1+lnyd2ydx2=0

Q: du d'u +5 d'u -2 dr5 - 1o du + 5u : 0 drs dr

A: Image is attached with detailed solution.

Q: y' + }xy = sin(x 4e¤2 y3 1

A:

Q: y' + y² = 3y tan x tan? x + 1

A:

Q: dy 4. x-+y = x²y² In x dx

A:

Q: (d) y +6y +13y=e³* cos 2x

A:

Q: y" + 4y = 3 csc²(2t)

A:

Q: dy 1 1. dx +3y= = e*y*

A:

Q: d²y 4. dx² 4 + y = 0,y(0) =" (0) = 4 +у %3D 0,у (0) dx dx

A: Suppose the solution of the form is y=erx .find y',y'' .…