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: а. (4x3 — 6ху^)dx + (4y- 6ху)dy %3D 0 b. 1 -(xdy- ydx)=0 x²+y? с. 1 (v²dx+x²dy)=0 (x2-у?) d. (x+y)dx…

A:

Q: (x + Y) dx +(y? + Inx) dy 0, is exact differential equation.

A:

Q: the indicial equation of the differential equation xy'' -x2y'+(1+2x)y=0

A: Question from differential equations.

Q: Find the differential equation of the following families of curves: y2(b+x)=x2(3b-x)

A: Given y2(b+x) = x2(3b-x)                 (1) Differentiate equation (1) with respect to x , we get…

Q: of y' = x²/(y + 1)?

A:

Q: Obtain in factored form of a linear differential equation with real, constant coefficients that is…

A:

Q: Solve the differential equation with subs equation : S y(s) = (s+2)² +1 O e?"(cos t – 2 sin t) O e2"…

A:

Q: Determine the type of differential equation given below: * 2x(у + 1)dx — уdx %3D 0

A: Given differential equation  2x(y+1)dy - ydx = 0 If the differential equation is in the form…

Q: Form the differential equation for the function x +2y = a sin3x - bcos3x а. Зу" - 18у %3D -9х O b.…

A: The second order differential equation for a function can be found by differentiating the function…

Q: d’y (b) dx + y =: dx 1+x

A:

Q: An ordinary differential equation of a horizontal string which is freely pinned at both ends is…

A: Given problem is :

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: y(s) = (s+2)² +1 e2" (cos t - 2 sin t) -2t e" (cost – 2 sin t) A.) B.) e-2"(cos t + 2 sin t) e2"…

A: Correct ans is option A

Q: Find the Differential equation by eliminating the arbitrary constant  Sin-1 x + sin-1 y = C

A: sin-1x+sin-1y=C

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…

Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

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.