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63
94 votes
11 answers

Calculating the integral $\int_{0}^{\infty} \frac{\cos x}{1+x^2}\mathrm{d}x$ without using complex analysis

calculus real-analysis integration definite-integrals improper-integrals Oct 26 at 9:04 Shing
math.stackexchange.com

82
73 votes
2 answers

Mathematical precise definition of a PDE being elliptic, parabolic or hyperbolic

pde Nov 26 '16 at 18:08 suomynonA
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23
22 votes
2 answers

PDEs on Manifolds

analysis differential-geometry pde Aug 23 '12 at 21:22 doraemonpaul
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24
21 votes
4 answers

Why separation of variables works in PDEs?

pde Nov 21 '13 at 9:08 Community
math.stackexchange.com

12
16 votes
3 answers

Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?

analysis ordinary-differential-equations pde lipschitz-functions Feb 21 '18 at 12:59 Community
math.stackexchange.com

12
14 votes
1 answer

What kinds of PDE can't be solved by separation of variables?

pde Jun 16 '13 at 18:01 Community
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5
11 votes
2 answers

Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$

calculus limits May 21 at 19:18 robjohn
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1
9 votes
2 answers

Name for a Particular (Parabolic) PDE

reference-request pde Jun 7 at 16:30 Community
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2
7 votes
6 answers

Verify the identity: $\tan^{-1} x +\tan^{-1} (1/x) = \pi /2$

trigonometry Aug 9 '16 at 4:14 Martin Sleziak
math.stackexchange.com

2
7 votes
1 answer

Number of zeroes of solution to $y''(x)+e^{x^2}y(x)=0$ in $[0,3π]$

ordinary-differential-equations Dec 30 '16 at 6:49 achille hui
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3
7 votes
0 answers

Solve ODE $y'' + (y')^2 + y = \ln(x)$

ordinary-differential-equations May 23 at 21:45 sudeep5221
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4
6 votes
1 answer

What is the 'linearization' of a PDE?

reference-request pde linearization Nov 13 '16 at 23:14 Glitch
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3
5 votes
1 answer

Laplace-Beltrami on a sphere

differential-geometry surfaces spherical-coordinates Dec 7 '17 at 8:49 shall.i.am
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2
5 votes
4 answers

How to come up with a counter example in linear algebra

linear-algebra examples-counterexamples Apr 20 '15 at 22:08 Community
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2
5 votes
1 answer

How to create theorem boxes

environments boxes tcolorbox Feb 29 '16 at 1:23 JP-Ellis
tex.stackexchange.com

7
4 votes
1 answer

Is it possible to compute the integral $\int_{0}^{\infty} \frac{\cos x}{1+x^2} \mathrm{d}x$ using ODE?

calculus real-analysis integration ordinary-differential-equations Dec 12 '17 at 11:31 Nosrati
math.stackexchange.com

2
4 votes
1 answer

Prove that $y_1(x)=\sin(x^2)$ can't be a solution for a linear homogeneous second order differential equation.

ordinary-differential-equations Nov 30 '15 at 18:57 Julián Aguirre
math.stackexchange.com

2
4 votes
1 answer

Properties of sin(x) and cos(x) from definition as solution to differential equation y''=-y

ordinary-differential-equations trigonometry definition Apr 24 '16 at 4:55 user5713492
math.stackexchange.com

1
4 votes
1 answer

Do both of these functions define the same branch of $\sqrt{z^2 - 1}$?

complex-analysis complex-numbers complex-integration branch-cuts Dec 26 '17 at 18:07 Eric Wofsey
math.stackexchange.com

3
3 votes
1 answer

If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute

matrices analysis exponential-function semigroup-of-operators Mar 12 '18 at 14:37 Dato Gochitashvili
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2
3 votes
2 answers

Bounding solutions of ODE

ordinary-differential-equations Oct 22 '17 at 21:22 Robert Lewis
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1
3 votes
1 answer

Solution to second order non constant differential equation without first derivative

ordinary-differential-equations Oct 24 '17 at 19:10 Nosrati
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2
2 votes
1 answer

Loophole? I'm getting 2 different answers when solving a differential equation in 2 different methods

integration ordinary-differential-equations Jan 6 '18 at 7:53 José Carlos Santos
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1
3 votes
2 answers

Dirichlet problem with odd function.

real-analysis pde May 15 at 19:21 pipenauss
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3
3 votes
1 answer

Solve Riccati equaiton $x'(t) + x^2(t) = \sin(t) + \cos(t)$

ordinary-differential-equations May 25 at 23:07 Jethro
math.stackexchange.com

2
2 votes
1 answer

Geometric interpretation of monotone operators on a Hilbert space

functional-analysis convex-analysis hilbert-spaces intuition monotone-functions Nov 26 '15 at 21:37 user147263
math.stackexchange.com

2
2 votes
3 answers

$\sin(t)$ solution of $\ddot{x}=-x$

ordinary-differential-equations Oct 13 '17 at 21:15 José Carlos Santos
math.stackexchange.com

3
2 votes
3 answers

Show that all solutions of $y'= \frac{xy+1}{x^2+1}$ are of the form $y=x+C\sqrt {1+x^2}$ without solving the ODE

ordinary-differential-equations Feb 27 '18 at 11:44 Abeer D
math.stackexchange.com

1
2 votes
0 answers

What if the highest order coefficient of a linear ODE is sometimes zero?

real-analysis ordinary-differential-equations singularity May 15 at 3:42 MathematicsStudent1122
math.stackexchange.com

2
1 vote
2 answers

How do the solutions to the wave and heat equations converge in general?

functional-analysis pde hilbert-spaces spectral-theory Aug 25 '12 at 22:11 doraemonpaul
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