# Search results for query: *

1. ### Cumbersome Trig integral

You've got a few errors in your integration. Integrating -2sin6x should be 1/3 cos6x and -sin12x should be 1/12 cos12x. The final answer seems alright surprisingly.
2. ### Series Circuit DIfferential Equation - My answer is coming out to be wrong

First off, Your entire method could not possibly work if E(t) is not simply a constant, but thankfully in this case it is. You only made one simple mistake when you integrated di/[E-2i]. you're missing a -1/2 in front of the ln|E-2i|.
3. ### Lim x->infinity

I approached the question by first factoring out x1/3 from the bracketted expression. with the remaining surdic expression, i rationalised the numerator in terms of cube roots so the numerator i would have [(x2 + x + a) - (x2 - b)] = x + a + b in it. I rearranged the x4/3 in the numerator to...
4. ### 2 differentials, one of which is almost solved

You did nothing wrong for the first problem. Just try plugging the terms into the original ODE again carefully. For the 2nd problem, make y' the subject and think about what happens when something is implicitly differentiated. I think the answer is ey + ex + exy = 0. Good luck.
5. ### Seemingly difficult complex arithmetic problem

What's so hard about this question? It only requires some very basic trigonometric identities and properties of moduli. Several Hints: To derive T, 1) e-i(theta) = cos(theta) - i sin(theta) 2) How does one divide 2 complex numbers (ie. (x1 + iy1)/(x2 + iy2) )...
6. ### Integral equation

i know you calculate the integral to obtain the constants, but I am just at a loss in doing what you both did. the solution to the ODE would be y = Ax + B. when inserted into the original equation, Ax + B = 1 + (int 0->1) (x-t)y(t)dt (A - (int 0->1)y(t)dt)x + (B - 1 + (int 0->1)...
7. ### Integral equation

I'm just wondering how did get these combinations for the constants after you've plugged your solution into the integration equation.
8. ### Need help solving the integral: (x^2)/(2^x)

This Integration Technique might be useful in your case: http://en.wikipedia.org/wiki/Integration_using_parametric_derivatives
9. ### Possibly impossible question?

obviously, one solution is t = 1.

11. ### Prove integral

I think you made a mistake typing it: It should be '+' in between the 2 fraction and the integral. Just do a simple Integration by parts without induction. Let dv=dx , u = 1/(1+x2)n In = x/(1+x2)n + 2n(integral)[x2/(1+x2)n+1]dx as 'x2 = 1 + x2 - 1', You should end up with: In =...
12. ### Solving 3xy^3 + (1+3x^2y^2)dy/dx=0: A Step-by-Step Guide

You won't need to rely upon integrating factors in this case. we know dy/dx = -3xy^3/(1 + 3x^2y^2) Thus: dx/dy = -1/3xy^3 - x/y Making a simple substitution of u = xy dx/dy = (y*du/dy - u)/y^2 when the substitution is made The equation should become separable.
13. ### Solving 3xy^3 + (1+3x^2y^2)dy/dx=0: A Step-by-Step Guide

For starters, it's y' + P(x)*y = q(x) For this to be true, the DE has to be linear. Do you think it is linear, separable or neither?
14. ### Calc 2 final tomorrow need help

Essentially this is using the chain rule whereby when: G(x) = (integral of f1(x) to f2(x) ) g(t) dt G'(x) = g(f2(x))*f2'(x) - g(f1(x))*f1'(x) so in your case, G'(x) = sin(-x^4)*2x - sin(-x^2)
15. ### Complex Variables

For the second question, a big hint is to equate equivalent terms. a + bi = c + di --> a = c, b = d Don't move things across the equals sign, but work on each side separately
16. ### Integral of problem

for question 2, You've got a problem with this question which u will find out once u find the indefinite integral. x can't equal to either 1 or 0.
17. ### 2nd order inhomogeneous ODE

what do you mean? In this integral problem, you'll have 3 constants: one you started with (c), one you attained from the first integration (k or C1), and the last from the final integration (A) Since you gave me pairs of values for x,T and T', the constants will result in a certain value...
18. ### Powers of Complex Numbers

Both the book and your answer is right - though technically the answers should be 32e^-i(1/2pi). remember, the range of principal argument is 0 < theta < pi (above the x-axis) & -pi < theta < 0 (below the x-axis). so whenever you get a value beyond these ranges you have to convert your...
19. ### 2nd order inhomogeneous ODE

This question has quite a few twists to it, especially if you want to get an explicit equation with T as the subject. i checked my solution and you get back to the original second order equation. dx/dT = 1/sqrt[2(k - ce^T) Where k is an arbitrary constant like you C1 to integrate this, i...
20. ### Powers of Complex Numbers

z = -1 + i = sqrt(2) cis(3/4 pi) z^10 = 2^5 cis (10 x 3/4 pi) {De Moivre's Theorem} = 32 cis (15/2 pi) = -32i
21. ### 2nd order inhomogeneous ODE

There's been one mistake running through it all... v = dT/dx NOT dx/dT I've worked out a solution but it doesn't fit with T(1) = T(-1) = 0 But it does work if x = 0, T = 0. No problems with T'(0) = 0. x = - sqrt(2/c) {ln|1 + sqrt(1 - e^T)| - 1/2 T} That's the best i could do.
22. ### Separation of Variables: How to integrate (x+2y)y'=1 y(0)=2?

I got a different answer using linear differential equations. dy/dx = 1/(x + 2y) dx/dy = x + 2y dx/dy - x = 2y The answer i got was: x = -2y -2 + 6e^(y-2) Differentiating it again returns me to the original differential
23. ### Help Solving a Diff. Equation: Ideas Needed

Try using the substitution v = x/y which is equivalent to vy = x So dx/dy = v + y*dv/dy Give it a try and see if it works.
24. ### Sequences, convergance and limits.

(n+3)^[1/(n+3)] is just the same as saying x^(1/x). x^(1/x) = e^(1/x lnx) the limit as x -> infinity, lim x^(1/x) = lim e^(1/x lnx) = e^lim (lnx / x) lim (lnx / x) = lim (1/x) {Le Hopital's rule} = 0 Thus, e^0 = 1 and the series is convergent