Nonlinear differential Definition and 65 Threads

hi, i am facing problem in solving the following differential equation. help me. y''+ayy'+b=0, where y is a function of x, 'a' & 'b' are constants. i have tried substituting y'=u, which implies u'=u*dy/dx, these substitution change the equation to first order but i found no...

As far as I know, for an n-th order homogeneous linear differential equation, there are n number of linearly independent solutions and the general solution to the equation is a linear combination of them. In the case of nth order homogeneous non-linear differential equation can it be shown that...

Suppose there is a nonlinear differential equation in y(x) of the form: y''(x)(c_1+a^2y(x)^2)+p_1(x)y'(x)^3-by(x)y'(x)^2+p_2'(x)(c_1+a^2y(x)^2)+hy(x)=0 Where prime denotes derivative with respect to the argument x; p_i are known variables, and c,a,b,h are constants. Is there any way to write...

Hi, I'm a PhD student in Operations Management, and I've stumbled across a differential equation while modeling an OM concept. I was wondering if you could help me with this differential equation, or direct me in a way that would help me solve it. The equation is...

Is there any theorem or result which tells us whether a given set of nonlinar coupled differential equation (ordinary/partial) will have unique solution set? I need to know the answer for a second order ODE set. I understand there may be some difficulty since in this case the integration...

Hello all, This is the first time I've stumbled across this site, but it appears to be extremely helpful. I am a meteorology grad student, and in my research, I have run across the following 2nd order non linear differential equation. It is of the form: y'' + a*y*y' + b*y=0 where a...

[Differential equation at the end; All the intermediary stuff is the problem behind it.] I was curious about finding the velocity function for a free-falling object using solely Newton's equations. Using the force diagram, I've deduced that m-mass g-gravitational constant f_net - net...

Hi all, Can anyone please give me an example of a nonlinear differential equation used to model a certain type of circuit? Thanks

Hello! I tried to prove, that ideal rope (see picture in attachment) has a shape of the function ch[x]. I finished with this equation [h'(x)]^2-h(x)\cdot h''(x)+1=0 Yes, when you try function h[x]=ch[x], you get 0 on the left side, but I have no clue how to solve this equation (find...

Hi all, I am more into physics than maths and I need you guys to please help me out. Also I am new to programming in MATLAB. I have done some but still I consider myself a novice. I need to solve the problem in MATLAB. So here is the problem.Its a 2 point BVP(boundary value problem) along...

I need some help with the problem that follows. Any help is highly appreciated. Problem: "Consider the initial value problem y^{\prime}=y^{1/3}, \mbox{ }y(0)=0 from Example 3 in the text. (a) Is there a solution that passes through the point (1,1)? If so, find it. (b) Is there a solution...

I need to solve the following second order nonlinear differential equation: z''(b) * [6(1 - f)z(b) + (1+f)b z'(b)] = (15 - 9 f)[z'(b)]^2 + [2(1 - f) z(b) z'(b)] / b + [4 f z'(b)^(5/2)] / b^(1/2) where f is a constant between [0,1]. initial conditions are z(0)=0 and z'(0)=0 I...

The problem is on competing species. For the problem, I am supposed to find the critical points. For each critical point, I need to find the eigenvalues and eigenvectors and classify the type of critical point and its stability. dx/dt = x(1.5 - x - 0.5y) dy/dt = y(2 - y -0.75x) I got...

Variable co-effiecients Linear Differential equation \frac{d^2 y}{dx^2} = c_1y(1-c_2x) any help? Is there a solution besides a series solution?

Having some troubles getting further in this system I'm trying to solve. The notebook's at http://www.gabrielwyner.com/fluids5.nb PDF form: http://www.gabrielwyner.com/fluids5.pdf I guess the most current problem involves mathematica complaining about DSolve[h'[t] = f[h[t],h[0]]] (with...