Recent content by the0

Homework Statement Find the set of functions from (-1,1)→ℝ which are solutions of: (x^{2}-1)\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}-4y = 0 Homework Equations The Attempt at a Solution There is a hint which says to use the change of variable: x=cos(θ) doing this I get...

Homework Statement Y'(u) = A(u)Y(u) V(u) is the general solution The question asks to show that if A(u) is antisymetric for all u i.e. ^{t}A(u) = -A(u) for all u Then ^{t}V(u).V(u) = I Homework Equations A hint says to use the fact that V(0) = I The Attempt at a Solution...

OK, thanks a lot! Right, am I correct in substituting the following: x = cos(θ) \frac{dy}{dx} = (\frac{-1}{sin(θ)})\frac{dy}{dθ} \frac{d^{2}y}{dx^{2}} = (\frac{-cos(θ)}{sin^{3}(θ)})\frac{d^{2}y}{dθ^{2}} ? If so, I get...

I've never come across that before :/ How can I use that to solve it? rearrange to give: y''+\frac{x}{(x+1)(x-1)}y'-\frac{4}{(x+1)(x-1)} = 0 ? Then I can't see why the change of variable hint has been given.

Homework Statement Find the set of functions from (-1,1)→ℝ which are solutions of: (x^{2}-1)y''+xy'-4y = 0 Homework Equations The Attempt at a Solution OK, I'm not really sure how to go about solving this equation, I have only previously attempted problems where the functions in...

Can the general solution already posted simply extend to I = (-1,+∞) ?? If so how can this be shown in detail? Also I don't yet understand what happens when we are considering ℝ Thanks for any help!

would simply multiplying by x solve this? i.e. y_{p} = e^{x}(Axsin(2x)+Bxcos(2x)+C+Dx+Ex^{2})

Yes I have studied this method (a little) however I am struggling to choose the right form for the particular solution: Should y_{p} = Asin(2x)+Bcos(2x)+e^{x}(C+Dx+Ex^{2}) work?

Homework Statement The problem is to solve: y''-2y'+5y = e^{x}(cos^{2}(x)+x^{2}) Homework Equations The Attempt at a Solution I (think I) have solved the associated homogeneous equation: y''-2y'+5y = 0 giving the solution as: y_{h} = e^{x}(C_{1}cos(2x)+C_{2}sin(2x))...

Homework Statement Given (E): (x+1)^{2}(xy'-y) = -(2x+1) Determine the set of applications from the interval I to ℝ which are solutions of (E) for: a) I = (0,+∞) b) I = (-1,0) c) I = (-∞,-1) d) I = (-1,+∞) e) I = ℝ The attempt at a solution I have...

I realized that it was that simple right after I posted it haha and I missed out the 2 in the original statement of the problem, my mistake, sorry about that. Thanks a lot!

I realized that it was that simple right after I posted it haha and I missed out the 2 in the original statement of the problem, my mistake, sorry about that. Thanks a lot!

Ok, thanks! So I get: xy' = (1-2x2)cot(y) ∴ y'tan(y) = (1-2x2)/x Then how do I go about integrating the left hand side?

Homework Statement Find functions y=y(x) defined on (-∞,0) or (0,+∞) which verify: xy'+(x2-1)cot(y)=0, y(x_0{})=y_0{} for x_0{}≠0 and cos(y_0{})≠0The Attempt at a Solution I'm really stuck on this one! Any help will be very much appreciated!