Consider Euler' s ordinary differential equation with the boundary conditions for unknown function y(x) in 0SxSe-1, and A= const (1+x)y"-(1+x)y'+Ay=0; y(0)=y(e-1)%3D0 where 'prime' stands for x-derivative, say, y' dy/dx. the multiple choice answers use notations: A= 7, nn =n², AA = 7, etc. O Find all the eigenfunctions y(x) for A=1 Q. Find all eigenfunctions y(x) for A>1. Hint: use notation A=1+p2. Q. Find all eigenfunctions and eigenvalues for A<1. Hint accept notation A=1-02 Q: Find all eigenvalues A, for A>1. Hint: use notation A=1+p2.

Q: State the order of the given ordinary differential equation. (2x - tan(17x))y"" - x²y" + 18y' =…

A: Given the ordinary differential equation is  2x-tan17xy'''-x2y''+18y'=18sinhx+16

Q: S[y] given by y = cosh æ + B sinhx, 0 0,

A:

Q: Is the following a homogenous differential equation? dy/dx = (x2y-y2x)/(x3-y3)

A: Let's find

Q: of y' = x²/(y + 1)?

A:

Q: d’y (b) dx + y =: dx 1+x

A:

Q: nd the solution of the differential equation = Z 3 + sin(z) with i dz

A: Given: dfdz=z-23+sin(z)f(0)=2

Q: Sketch the direction or slope field of the differential equation. Be sure to show any “trends" and…

A: Given differential equation is y'=x-2y+1                   (i) Direction field of the given eq. (i)…

Q: ou are given the following differential equation:  (1/x4)(dy/dx) + (1/x2)y = x5, x > 0.  What…

A: Given differential equation A differential equation of the form is a linear differential equation…

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.