List questions from initial-value-problems

Published on 12 Apr 2026 - 21:58

249

Views

Proving a differential equation has a unique solution, where $f(t,x)$ is decreasing.

Published on 14 Apr 2026 - 13:44

446

Views

Solution to ODE $ x'= x^3+ \sin( t)$ and showing it has a periodic solution

Published on 16 Apr 2026 - 11:42

148

Views

Proving an IVT has a local unique solution

Published on 14 Apr 2026 - 19:48

35

Views

Wave equation: ensuring a minimal value by setting a constraint on initial conditions

Published on 26 Mar 2026 - 2:06

39

Views

Proving existence and uniqueness of solutions of this IVP: $x'(t)=f(x(t))+\sin(t)$, with $x(0)=0$ and $f\in C^2$

Published on 17 Apr 2026 - 0:33

78

Views

Best Lipschitz constant for IVP with two variables $u$ and $t$ with an initial condition and interval for $t$?

Published on 16 Apr 2026 - 2:37

98

Views

How to solve the differential equation $y''=\frac{y'}{y}$

Published on 25 Mar 2026 - 17:39

215

Views

Maximal interval of existence for $x'=\frac{xt}{\sqrt{x^2+1}}$

Published on 17 Apr 2026 - 1:09

82

Views

Existence and uniqueness of IVP solution

Published on 14 Apr 2026 - 2:18

570

Views

Initial value problem using variation of parameter.

Published on 12 Apr 2026 - 8:39

54

Views

ODE theorem about solutions related to improper integral

Published on 10 Apr 2026 - 23:40

267

Views

Unique solvability of ODE

Published on 13 Apr 2026 - 22:25

165

Views

All solutions of the ODE

Published on 30 Apr 2026 - 8:52

100

Views

Homogenous differential equation and its solution

Published on 09 Apr 2026 - 5:46

List Question

Solve the following wave initial value problem by using the D'Alembert's formula

Proving a differential equation has a unique solution, where $f(t,x)$ is decreasing.

Solution to ODE $ x'= x^3+ \sin( t)$ and showing it has a periodic solution

Proving an IVT has a local unique solution

Wave equation: ensuring a minimal value by setting a constraint on initial conditions

Proving existence and uniqueness of solutions of this IVP: $x'(t)=f(x(t))+\sin(t)$, with $x(0)=0$ and $f\in C^2$

Best Lipschitz constant for IVP with two variables $u$ and $t$ with an initial condition and interval for $t$?

How to solve the differential equation $y''=\frac{y'}{y}$

Maximal interval of existence for $x'=\frac{xt}{\sqrt{x^2+1}}$

Existence and uniqueness of IVP solution

Initial value problem using variation of parameter.

ODE theorem about solutions related to improper integral

Unique solvability of ODE

All solutions of the ODE

Homogenous differential equation and its solution

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