Questions tagged [reduction-of-order-ode]

Question 1

What are the conditions under which the formula I've given below for an inhomogeneous reducible 2nd‐order ODE is valid? I have the second‐order inhomogeneous ODE $$ y''(t) \;+\; h(t)\,y'(t)\;+\;q(t)\,...

Question 2

Given question Given $y=x$ is a solution of $6x^3y’’’ - 24x^2y’’ + 48xy’-48y = 0$. Find the general solution if $x>0$. My work Since we are given that $y = x$ is a solution, my first approach would ...

Question 3

Need help solving this differential equation$$xy''+(x+l)y'+ly=0$$ where $l\in \mathbb{R}$\ I tried using the Frobenius method. $x_0=0$ is a regular singular point and Assume that we have the solution ...

Question 4

If $y_{1}(x) = \frac{\sin(x)}{\sqrt(x)}$ is one solution of the differential equation $$x^2y'' +xy' + (x^2-\frac{1}{4})y = 0$$ find the second solution $y_{2}(x)$. My effort using Wronskian The ...

Question 5

Given the equation y'' + 2y' + y = 0 and the solution y1 = ${xe}^{-x}$. Solve for a second solution $y_2$. I've solved it twice and get $y_2 = {xe}^{-x}(-{x}^{-1}+c)$ , but that's not being counted ...

Question 6

This is the question, given that; $y_1 = x$ $$ (x^2+1)y''-2xy' +2y = 0 $$ other form $$ y''-\dfrac {2x}{(x^2+1)}y' +\dfrac {2}{(x^2+1)}y = 0 $$ using the formula $y_2 = y_1 \int e^{-\int p(x)dx} / y_1^...

Question 7

How to reduce the following O.D.E. into first order? $v v_{yyy} + 2 v v_{yy}-v_{y}v_{yy} + v_{y} v^3 + v_y v -v_{y}^2 = 0$, where $v=v(y)$ and $v_{y}$ is the derivative w.r.t. $y$. I tried it by ...

Question 8

I want to solve $y'' +y^3 = 0$ with the boundary conditions $y(0) = a$ and $y(k) = b$. My goal is to reduce this problem to $y' +y^2 = 0$ while solving but I'm not sure it can be done. I tried ...

Question 9

How to reduce the following O.D.E. into first order? $$(vv_{xxx}-v_{x}v_{xx})g^2 + v^3 v_x = 0, \tag{1}$$ where $v=v(x)$ and $v_{x}$ is the derivative w.r.t $x$, $g$ is a constant. After integration, ...

Question 10

How can we reduce this differential equation into first-order differential equation? $\left( {\frac {\rm d}{{\rm d}z}}U \left( z \right) \right) ^{3}{ \frac {{\rm d}^{2}}{{\rm d}{z}^{2}}}U \left( z \...

Question 11

I am trying to determine how to turn these two 2nd order ODEs into a system of four 1st order ODEs with initial conditions. Afterwards, I am to turn it into a matrix. eqn 1: $$3.2\theta''_1 + 1.44[\...

Question 12

I am trying to perform model reduction on a system of algebraic equations by reducing the number of variables in the system. In doing so I am not trying to remove equations from the system, rather I ...

Question 13

Solve the equation $ty''-y'+4t^3y=0, t>0$ given that $\sin(t^2)$ is a solution. (I am aware that this has been asked before but the answers did not help me). My attempt: I want to use reduction of ...

Question 14

How the following 4th order linear differential equation can be reduced to two 2nd order differential equations, if possible. $a$ and $b$ are constants. $$X^2 Y^{(4)}(X) + 2 (a+2) X Y^{(3)}(X) + (...

Question 15

For the reduction of order method, we are supposed to guess a solution, $y_1$, and assume that the second solution (this will be second order as the title shows) is of the form $y_2=uy_1$. But I'm ...

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Questions tagged [reduction-of-order-ode]

Question about conditions required for an alternate method of solving reducible 2nd order ODEs.

When solving a third-order ODE using reduction of order, what happens when the v’ term drops out

Frobenius method for solving differential equation

How can I solve a Bessel equation with Reduction of order?

Reduction of Order to solve, but can't get right answer

Simple second order equation to be solved by reduction of order

How to reduce O.D.E. into first order? [closed]

Reduction of Order to Solve $y'' =-y^{3}$

How to reduce the ODE to first order?

How to reduce this differential equation into first-order differential equation?

Reduction of Order for two 2nd Order ODEs to a system of four 1st order ODE with Initial Conditions and sine functions

Error Reduction of System of OverDetermined Algebraic Equations

Solving a linear ODE of second order by reducing the order

Reducing the order of differential equations

Solve the ODE $y y''=3(y')^2$ using Reduction of Order

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