3. Given that y₁ = t−¹ is a solution of 2t²y" + 3ty' — y=0, t>0, a) Substitute y = v(t)y₁(t) into the differential equation and simplify.

Q: Find the general solution to the differential equation y'' - 4y' + 5y = 0.

A: Here we find the general solution of the differential equationy''-4y'+5y=0-1

Q: Solve the differential equation y" + 16y 2cos z.

A:

Q: Find the general solution of the differential equation. y" – 7y" – 49y' + 343y = 0. NOTE: Use c1, cg…

A:

Q: What is the general solution to the linear differential equation? y' − 3y = 2

A:

Q: Find the general solution of the differential equation. y"" - 3y"-9y' + 27y= 0. NOTE: Use c₁, c₂ and…

A: The  given equation  is                                      Then, auxiliary equation  is…

Q: Find the general solution to the differential equation y" – 4y' + 4y = e²r + x² .

A: Given differential equation is

Q: yp given that yc = c1e6x + c2 xe6x if the differential equation is: y'' - 12y' + 36y = -6cos(2x)

A:

Q: Find

A:

Q: Find a particular solution (i.e. any solution at all) of the differential equation y' – 14y + 45y =…

A: The solution is given as

Q: Find every nonzero solution of the differential equation y = y +2y°.

A:

Q: Determine whether the given function is a solution of the differential equation. y = √√√x; xy' - y =…

A: Given a differential equation xy'-y=0. To determine whether function y=x is a solution of the…