Find the value of p(x), q(x) and r(x) in the Sturm-Liouville Boundary Value problem dy dy A +3x dx y=0, y(0) = 0 and y(1) = o A) p(x) = 5x ,q(x) = -3 and r(x) = = %3D B) p(x) = 5x, q(x) = 3x and r(x) = -- %3D %3D C) p(x) = 5x, q(x) = 3 and r(x) = 4 %3D D) p(x) = 5,q(x) = 3 and r(x) = 8 E) none of above

Q: 4. For y' = y3 +y² – 6y, Find the critical points. Draw a phase diagram and mark the critical points…

A: Given y'=y3+y2-6y Given a differential equation y'=fy a point y0 is said to be a critical point if…

Q: Problem 4. Using Euler's Method (h = dx = 0.2, xn = 1.5), find y(xn) for the boundary value problem…

A: From the given problem:   y'=1x2+y2y0.5=0.5⇒x0=0.5 & y0=0.5   So,…

Q: 1. Determine the type and stability of the critical points of the homogeneous systems: dx (a) = x –…

A: we have to check stability of critical points

Q: Determine the type and stability of the critical points of the homogeneous systems: dx = x - 2y dt…

A: We have to determine the type and stability of the critical points of the homogeneous systems.

Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = . √3 2…

A:

Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: 1) Solve the Boundary Value Problem. y" + y = 0, y(0) = 1, y(z)=1

A:

Q: Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the…

A:

Q: (x-2)²(x³-4) y = Vx2+1 dy If then equals to : dx O y [2/(x-2)+(3x^2)/(x^3-4)-2x/(3x^2+3)] O…

A: The formulas which are used to solve the above problem are stated with the solution.

Q: How we can obtain the numerical solution of the nonlinear boundary value problem y" = y²y', 0≤t≤1…

A: Given y''=y2y', 0≤t≤1y0=0, y1=0 and t0=0, t1, t2, t3, t4, t5=1

Q: 2.9. (a) Solve the integral .. (dx.draw) 3N and use it to determine the "volume" of the relevant…

A: V3w=∫0≤∑i=13Nxi≤R∫ (dx1,…dx3N) Obviously, the volume vn will be propositional to Rn

Q: Express the solution of the given initial value problem in terms of convolutional integral. A. y" +y…

A: Given differential equation is y''+y'+54y=1-u(t-π);         We have to express the solution of the…

Q: Consider the linear system : dx 2х — 2у dt dy - 2x + Y dt with initial conditions x(0) 0 and y(0) =…

A:

Q: Find the solution of the given boundary value problem d²x dx 6x = 0, x(0) = 1, x'(0) = 1 dt %3D - -…

A: In this question, we solve the differential equation using initial conditions.

Q: 2. Give the general solution of xy'dy = (x³ +y³)dx in explicit form.

A:

Q: Obtain a family of solution 1. (5v - u)du + (3v -7u)dv = 0 2. (x -y ln y + y ln x)dx + x(ln y - ln…

A: Since, you have posted multiple questions, as per guidelines we will solve only first question. If…

Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = -1/ 1-…

A: The given differential equation,1-y2dx-1-x2dy=0, y0=12

Q: 15. Find the value(s) of y such that the solution of the initial-value problem y" – 4 y = sin x;…

A:

Q: Consider a spring-mass system described by the initial value problem y" +0.25y' + 2y = 2 cos(wt),…

A:

Q: Consider the Initial Value Problem: y = y + 3x – 5, y(1) = -2. An approximation of y(1.2) with step…

A:

Q: The Particular solution of the boundary value problem (D+4)y=Q,with y(0)-2,- 0 is a) y=-2 cos 2x b)…

A: To find the particular solution to the below initial value problem. D2+4y=0, y0=−2, yπ2=0

Q: 1.) Find a Frobenius type solution around the singular point of x = 0 . *ア+(*+x)ーy=0

A: Frobenius series method

Q: Consider the system of differential equations dx = 0.3x – 0.02xy - dt dy 0.2y + 0.016xy dt Where x…

A:

Q: Find an explicit solution of the given initial-value problem. x2 dy = y - %3D у — ху, у(-1) %3D -1…

A: Firstly we will solve the given differential equation by using variable separable form then…

Q: Express the solution of the initial value problem dy 2x- dx as an integral = y + 2x cos x, y(1)= 0

A: Simplify and convert in linear equation.

Q: 2- Find the solution of the partial differential equation =u, -2 with boundary conditions u(x,0) 0…

A:

Q: Find an explicit solution of the given initial-value problem. +²dy x=y=xy, y(-1) = -4 dx y =

A:

Q: 2. Consider y+2-c y+1+cy, where e is a positive constant. For what values of e will the solution to…

A: Given yt+2-cyt+1+cyt

Q: 6. Find the general solution of (cos cos y +ycos x) dx+ (sin sin x – x sin sin y ) dy = 0 A. x cos y…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: Show that (0, 0) is an unstable critical point for the following system: 2xy + x3, 1 -x2 + y°. de dy…

A: We will find Jacobian matrix  for system of differential equation Then depend on eigen values of…

Q: 2. Find the first three approximations yı, y2, y3 using Euler's method for the initial value problem…

A: Let's find.

Q: Use Euler's method with step size 0.1 to estimate y(0.5), and z(0.5) where y(x) and z(x) form the…

A: Given differential equation are, y'=3x+z2, y0=-1z'=-4x+y2, z0=1.

Q: Find the general solution of the given system. dx/dt = -(5/2)x + 4y dy/dt = (3/4)x - 3y =________

A:

Q: Find the solution of the initial value problem subject to the indicated initial condition in terms…

A: Given 2x (x2+y)dx = d y , y(0) = -1

Q: In Problems 1 to 12 find the general solution dx = -4x + 2y dt dy of the given system. 5 x + 2y 2 dt

A:

Q: Find an explicit solution of the given initial-value problem. 1 √1-y² dx √1-x² dy = 0, y(0) = = y =

A:

Q: Minimize F(y, u) = f¿u²(t) dt under ý = -2y + u with y(0) = 1, y(1) = 0. Is your solution unique?

A:

Q: Consider the system dx dy 1+3y, dt -1– 5x? dt a) Find all the critical points (equilibrium…

A: Critical points

Q: 1.) Use the following methods to solve the boundary value problem: - 2- y +x = 0 dx2 with boundary…

A:

Q: 3. Use Finite-Difference method to solve the boundary value problem dy dy +x dr+y= 3x² + 4x + 6 dx…

A:

Q: Find an explicit solution of the given initial-value problem. √1-y² dx - √1-x² dy = 0, y(0) = 113 2…

A: Here in this question, we have to find out the solution to the given differential equation.

Q: Find the general solution of the DE dyldx = (x + y) / x. O y = (x^2)ln(Cx) O y = (x^3)ln(Cx) O y =…

A:

Q: 3. Find the general solution of the system: dx = x + y dt dy -2x – Y dt

A: Given dxdt=x+y and dydt=-2x-y

Q: Consider the initial value problem {y′−3y=6, {y(0)=1. What is the limit of y(x) as x approaches −∞?

A:

Q: 2. Give the general solution of xy dy = (x³ + y³)dx in explicit form.

A:

Q: It is a standard form and general solution for variable separable type. Standard Form: P (x) dx + Q…

A: Please refer the attached image for complete solution. THANKYOU.

Q: (1 – xy)-2 dx + [y² + x²(1 – xy)¯2] dy = 0; when x = 4, y = 1.

A:

Q: The steady-state temperature, u(x, y), across a thin rectangular plate is governed by the following…

A: The given problem is to find the general solution for the given partial differential equation with…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.