Question

Using the method of undetermined coefficients, find the general solution of the DE yiv - 2ym + 2yn. = 3e-x + 2e-x x + e-x sinx.

13 Feb 2018
Answer :
Word Count : 370
The given differential equation is: \[ y^{(4)} - 2y^{(m)} + 2y^{(n)} = 3e^{-x} + 2e^{-x}x + e^{-x}\sin(x) \] We can solve this using the method of undetermined coefficients. However, we need to clarify a few things: 1. The expression contains terms like \(y^{(m)}\) and \(y^{(n)}\). To proceed, I'll assume that the correct form of the equation is: \[ y^{(4)} - 2y'' + 2y' = 3e^{-x} + 2xe^{-x} + e^{-x}\sin(x) \] If this assumption is correct, we can solve this as follows: ### Step 1: Solve the homogeneous equation The homogeneous part of the equation is: \[ y^{(4)} - 2y'' +
_________ __________ ________ _______ _____ _____ ______ ________ ____ ___ __________.
_____ ______ _________ ____ ____ _____ ____ ____.
_________ ___ _______ __________ _________.
______ _____ _____ ______ _________.
__________ _________ __________ __________ __________.
_______ _______ _______ _____ __________ __________ ______ ____ __________ ____ ________ ___.
_________ _______ _________ ________ __________ ________ _________ _________ ____.
________ ___ ____ ____ _______.
____ __________ __________ _________ ______ _____ _____ ____.
_______ ____ ________ ____ _________ _____ ____ ______ ______.
_________ ______ ________ __________ ____ _____ ___ _________ ________ _________ _____.
_____ ____ _____ _________ _________ _________ __________ __________.
__________ _______ ________ ________ _______ ______ ___ ______ _____ _____ _________.
____ ______ _________ _______ _________.
________ ________ ____ __________ ______ ________ _____ _____ _________.
_________ ______ __________ ____ _____ ____ ________ ____.
__________ ___ ___ _________ ________ ____ ______ _______ __________ ________ ___ ______.
____ _________ ____ ______ ____ __________ _______ _____ _________.
___ ______ __________ __________ ______ ____.
______ ___ _______ _______ ____ _________.
_____ ___ __________ _________ ______ __________ __________.
________ __________ _____ ________ _____ ______ ________ ______ _______.
_____ ___ _________ __________ ________ _______ ___ _______ _______ ______ ____.
______ _____ _________ ___ _______ _________ __________ ________.
__________ __________ _________ ___ _________ _______ ___.
____ _________ ____ ________ ___ ______ ___.
_________ ___ ____ _______ _______ ____ ___ _________ _______ ___ _____.
_____ ______ ____ _________ ___ __________ __________ _____ __________ _______.
_____ _______ ________ ____ _______ _____ ____.
_____ ___ _________ __________ _________.
_____ ____ _______ _________ __________ ______ ___.
________ _____ ___ ____ ________ ____ ________ __________ _____ ________ ___ _____.
_________ __________ ________ __________ ______ __________ ________.
IGNOU ACADEMY
Your IGNOU journey, made easier.
  • Solved Assignments
  • Study Notes
  • Guess Papers
  • Question Papers
Call Us WhatsApp
STUDY • PREPARE • SUCCEED
Skip in 10
Related Questions

Classify the following as true or false giving reasons for your answers..
i). For the IVP, \frac{dy} {dx } = f(x,y), y(x0) = y0 , the continuity of f(x,y) and \frac{\partial f}{\partial y }guarantees the unique solution of the problem.
ii). Equations \frac{d^2y}{dx^2} - 2x \frac{dx}{dx} + x^2y = e\tfrac{x^2}{2}  and  \frac{d^2y}{dx^2} + y =1
have the same normal form.
iii). Equation cos(x + y) p + sin(x + y)q = z2 + z is a quasi-linear equation.

iv). \frac{\partial ^2z}{\partial x^2} \frac{\partial ^2z}{\partial y^2} - (\frac{\partial ^2z}{\partial x\partial y})^2 = 0 is a non -linear PDE.

v). Every solution of the ordinary differential equation (D2 + 1)2 y = 0 is bounded on [0, ∞] .

Solve the following differential equations

a). sin -1(dy/dx) = x + y

b). (1 + y2)dx = (tan-1 y - x)dy

c). (D - 1)2(D2 + 1)2 y = sin2(\frac{x}{2}) + e^x +x

d). 2x^2y(\frac{d^2y}{dx^2}) + 4y^2 = x^2(\frac{dy}{dx})^2 + 2xy (\frac{dy}{dx})

 

 

 

A tightly stretched string with fixed end points x = 0 and x = l is initially in a position
given by y = y0sin3 (\frac{\pi x}{l}) . It is released from rest from the initial position. Find the displacement y(x,t).

Find the integral surface of the PDE (x - y)p + (y - x - z) q = z

Find the value of n for which the equation (n - 1)2 uxx  - y2n uyy = ny2n-1 uy is parabolic or hyperbolic.

Identify the following differential equations and hence solve them
i). y' = - \frac{4}{x^2} - \frac{y}{x} + y^2

ii). y = xy' + 1 - In y'.

Find the complete integral of the equation  
(\frac{\partial z}{\partial x1})(\frac{\partial z}{\partial x^2})(\frac{\partial z}{\partial xz}) = z2 x1 x2 x3.

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers
Login
Top
📞
Call Support Instant phone assistance IGNOU MTE 8 2018 - Using the method of undetermined coefficients, find the general soluti | IGNOU Academy
→
🟢
WhatsApp Chat Fast live messaging
→
Email Us Business enquiries & support
→