Question

Solve $U_{tt}=a U_{xx}$ when a<0.

score 79 · Answer 1 · 2026-03-22 12:39:44

79

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Solve $U_{tt}=a U_{xx}$ when a<0.

Published on 22 Mar 2026 - 12:39

score 79 · Answer 2 · 2026-03-20 07:49:47

79

Views

Solving $y''+\dfrac{\varepsilon y'}{y^2} - y' = 0, \, y(-\infty)=1$ and $y(\infty) = \varepsilon$

Published on 20 Mar 2026 - 7:49

score 412 · Answer 3 · 2026-03-22 10:04:35

412

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Solve $u_t+3uu_x=0$ , $u(x,0)=\left\{\begin{matrix} 2 & x<1\\ 0& x>1 \end{matrix}\right.$

Published on 22 Mar 2026 - 10:04

score 133 · Answer 4 · 2026-03-20 04:08:16

133

Views

Imposing a condition that is not boundary or initial in the 1D heat equation

Published on 20 Mar 2026 - 4:08

score 1.9k · Answer 5 · 2026-03-20 09:26:59

1.9k

Views

Solve the initial value problem (ODE) and determine how the interval on which its solution exists depends on the initial value?

Published on 20 Mar 2026 - 9:26

score 482 · Answer 6 · 2026-03-20 02:46:07

482

Views

The IVP $\begin{cases}\dot{x}=x^3+e^{-t^2}\\x(0)=1\end{cases}$ possesses a solution in $I=(-1/9,1/9)$

Published on 20 Mar 2026 - 2:46

score 416 · Answer 7 · 2026-03-20 10:05:18

416

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Prove that an IVP with discontinuous $f(t,x)$ has a solution for all $(t_0,x_0)$

Published on 20 Mar 2026 - 10:05

score 99 · Answer 8 · 2026-03-20 01:22:02

99

Views

Let $\dot{x}=\arctan(x(t)\cdot t)$, $x(t_0)=x_0$ be an IVP. Prove that if $x_0<0$, then $x(t)<0$ for all $\mathbb{R}$

Published on 20 Mar 2026 - 1:22

score 412 · Answer 9 · 2026-03-20 10:49:12

412

Views

Continuity of solutions of an ODE with respect to initial conditions: example

Published on 20 Mar 2026 - 10:49

score 351 · Answer 10 · 2026-03-22 05:32:41

351

Views

Differentiable dependence on initial conditions and parameters of an ODE

Published on 22 Mar 2026 - 5:32

score 48 · Answer 11 · 2026-03-20 06:25:06

48

Views

Which equation satisfies $\partial\phi_{t_0}$ and under what initial conditions?

Published on 20 Mar 2026 - 6:25

score 1k · Answer 12 · 2026-03-23 23:55:13

1k

Views

Solve the initial value problem: ODE with discontinuous coefficients?

Published on 23 Mar 2026 - 23:55

score 96 · Answer 13 · 2026-03-24 12:56:04

96

Views

Solve the given initial value problem and determine approximately the interval of existence?

Published on 24 Mar 2026 - 12:56

score 460 · Answer 14 · 2026-03-24 12:08:29

460

Views

A first order non-homogeneous initial value problem

Published on 24 Mar 2026 - 12:08

score 38 · Answer 15 · 2026-03-24 05:11:04

38

Views

Moving constants around during separation of variables

Published on 24 Mar 2026 - 5:11

List Question

Solve $U_{tt}=a U_{xx}$ when a<0.

Solving $y''+\dfrac{\varepsilon y'}{y^2} - y' = 0, \, y(-\infty)=1$ and $y(\infty) = \varepsilon$

Solve $u_t+3uu_x=0$ , $u(x,0)=\left\{\begin{matrix} 2 & x<1\\ 0& x>1 \end{matrix}\right.$

Imposing a condition that is not boundary or initial in the 1D heat equation

Solve the initial value problem (ODE) and determine how the interval on which its solution exists depends on the initial value?

The IVP $\begin{cases}\dot{x}=x^3+e^{-t^2}\\x(0)=1\end{cases}$ possesses a solution in $I=(-1/9,1/9)$

Prove that an IVP with discontinuous $f(t,x)$ has a solution for all $(t_0,x_0)$

Let $\dot{x}=\arctan(x(t)\cdot t)$, $x(t_0)=x_0$ be an IVP. Prove that if $x_0<0$, then $x(t)<0$ for all $\mathbb{R}$

Continuity of solutions of an ODE with respect to initial conditions: example

Differentiable dependence on initial conditions and parameters of an ODE

Which equation satisfies $\partial\phi_{t_0}$ and under what initial conditions?

Solve the initial value problem: ODE with discontinuous coefficients?

Solve the given initial value problem and determine approximately the interval of existence?

A first order non-homogeneous initial value problem

Moving constants around during separation of variables

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