3. (a) Find the eigenvalues and eigenfunctions of the boundary-value problem x2y'' + xy' + (lamda)y = 0,  y(1) = 0,  y(5) = 0 (b) Put the differential equation in self-adjoint form. (c) Give an orthogonality relation.

Q: 3. Consider the second order differential equation _dx +7. + 6x = 0. dt2 dt (a) Convert the equation…

A: Given is the second order homogeneous second order differential equation: x''+7x'+6x=0 let us first…

Q: Consider the differential equation d²x dx + b. + cx = 0, dt (9.4.5) di2 where b and c are constants.

A:

Q: The type of the partial differential equation du 2- ởu o'u =0 is +6- +3

A:

Q: Determine a basis for the solution spaceof the given differential equation. y′′ + 2y′ − 3y = 0.

A:

Q: 1. Show that the partial differential equation 3u, – 7u, = 0 has a solution of the form u(x, y) =…

A:

Q: Discretize the differential equation y" – 2y' + 4ty = 2t, y(-1) = -2, y(0) : -2 with step-size h %3D…

A:

Q: 3. Find solution of the differential equation; x "- 5x'+ 6x 6t-4 using Laplace transforms for the…

A:

Q: 1. Given the second order partial differential equation 4ux + 2uxy + Uyy+ xyUx – Uy+ u = 0. (a)…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: The partial differential equation 5x + 8y- = 7+ e10z is elliptic if .......... O 1. x > 0 and y 0 O…

A: We have to choose the correct answer

Q: 1. Reduce to two ordinary differential equations, one an eigenvalue problem, the other having one…

A:

Q: Make a phase diagram indicating whether the critical points correspond to an attractor or a repeller…

A: We need to create a phase diagram (slope diagram) and analyse its behaviour at the critical point.

Q: 1. The partial differential equation a²u azu ди, əx2 * ay2 = uy is classified as a) linear; 4th…

A: Given the partial differential equation

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: (1) let the differential equation be y''-8y'-15y=0 auxillary equation D2-8D-15y=0 now, ⇒m2-8m-15=0…

Q: y - 5y + 6y = e2t

A:

Q: 1 y" + 3 y + 2 y 1+ et

A:

Q: 1. Show that u(x,t)= etsin kx satisfies the partial differential equation_u₁ = α² uxx

A:

Q: Solve the first order inhomogeneous differential equation with constant coefficients using the x'=…

A: first we will convert the system into matrix form then using the coefficient matrix we will find…

Q: Example 9: Obtain the differential equation of the co-axial circles of the svstem x² +y² + 2ax+c² =…

A: Answer:

Q: Show that u(x, y) = xy is a solution of 2x- + y = 2x %3D дхду ду?

A:

Q: у + Зу +2 у %3D 1+ e

A: Given the given differential equation is y"+3y'+2y=11+et

Q: 4. Solve the partial differential equation (D² - DD' -2D2)z = (2x²+xy-y²) sin(xy) - cos(xy).…

A: Introduction: Like ordinary differential equation, partial differential equation can also be…

Q: 8. Suppose y1 and y2 are linearly independent, and the Wronskian of them, W (y1, Y2), is identically…

A:

Q: Convert the differential equation u - 5u' – 2u = et into a system of first order equations by…

A: We need to convert the differential equation u"-5u'-2u=e4t by letting x=u and y=u'

Q: If the auxiliary roots of a certain homogeneous linear differential equation are 2 + 31, #3i, +31,…

A:

Q: Find the general solution for the partial differential equation Uyy + 4 uy – 4u = 0

A: given a partial differential equation  uxx-uyy+4uy-4u=0   ...i claim  to find general solution

Q: Determine whether the given first-order differential equation is linear in the indicated dependent…

A:

Q: Find the solution of the partial differential equation 2 Uxy= -3U %3D

A:

Q: Suppose that the differential equation x' = Ax is such that A is a 2 × 2 matrix with (1) eigenvalues…

A:

Q: 3. A coupled mass-spring system is described by the differential equations x = -x, + x2 x- 2x, = 0…

A:

Q: da 3.2x + 0.75y, dt dy 1.66667x + 1.2y. dt For this system, the smaller eigenvalue is and the larger…

A: step:-1 Given system of differential equation is dxdt=3.2 x + 0.75 ydydt=1.66667 x + 1.2 y Take…

Q: Find the general solution for the system of differential equations. x' = -3x – 2y y' = 2x + y Use…

A: Consider the given differential equation.

Q: Find the solution of the partial differential equation- -8 0: ax2 ay? by variable separable method

A: Consider the given: ∂2z∂x2−8∂2z∂y2=0. Assume z(x,y)=X(x)Y(y). Therefore, ∂2z∂x2=X''Y and…

Q: Consider the eigenvalue problem y" + 2y' + ày = 0; y(0) = y(1) = 0. Show that the nth positive…

A: The auxiliary equation for the given differential equation is:

Q: If the auxiliary equation associated with a homogeneous linear differential equation with constant…

A:

Q: 9t y - 9 y = e3t

A:

Q: In the differential equation (2x+3y-5)dx+(3x- y-2)dy=0, the lines 2x+3y-5 =0 and 3x- y-2 =0…

A: This question can be solved using the concept of solving two linear equation.

Q: Solve the second order differential equation ÿ + ỷ – 6y = 8e* + 3x 1 A:y = ce2x + c2e-3x + 2e* + 12…

A:

Q: and find the solution surface Uxx Indicate the type of partial differential equation 3 +10 Uxy + 3…

A: Given differential equation is 3uxx+10uxy+3uyy=0 First need to identify the type of the differential…

Q: 2. Sketch the phase line and identify the equilibrium points for the differential equation dy - 3y…

A:

Q: Determine whether the Theorem 1.2.2 guarantees that the differential equation y' = Vy2 – 9 possesses…

A: We have to solve given problem:

Q: Find the eigenfunction assuming the second case for the given boundary value problem. y" +ly = 0…

A: The given problem is to solve the given boundary value problem y"+λy=0, with the given boundary…

Q: A dynamic system is represented by the following differential equation. y" - y' - 2 sin y = u(t),…

A:

Q: Eliminate the arbitrary constants indicated in brackets from the following equation and form…

A: Given: The following equation, 1ez-x2y=ax2y2+by ;a,b.

Q: (2) ( Consider the following system of differential equation, with time domain t e (0,1): x' = -2x +…

A: As given by the question There are given that the system of differential equation:…

Q: 8. Suppose y1 and y2 are linearly independent, and the Wronskian of them, W(y1, Y2), is identically…

A:

Q: る=1 For the system of differential equations below the eigenvalues are: 2=4 dx = 2x+2y dt %3D dy…

A:

Q: Solve the partial differential equation of ?2?????=6??2+3sin(?)+?−?cos(?), subject to the boundary…

A:

Q: Find the critical points and draw phase portrait of the given autonomous first- order differential…

A: Using the Zero Factor Principle: If a·b=0, then a=0 or b=0. The region above or below the…

Q: 3. Consider the second order differential equation d²x dx +7 + 6x = 0. dt2 dt (a) Convert the…

A: "Since,you have posted a question with multiple sub-parts,we will solve the first three sub-parts…

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.