New posts in Ordinary Differential Equations

How to calculate $\int _{-\infty }^{\infty }\frac{x\sin \left(x\right)}{1+x^4}\,dx$

Two methods are giving two different answers to the this differential equation : $\frac{dy}{dx}=\frac{1}{2} \frac{d(\sin ^{-1}(f(x))}{dx}$

Is there a reason it is so rare we can solve differential equations?

Solve the initial value problem: $\frac{dy}{dx} = e^{x+y}$, given $y(0)=0$.

Solving $\left(x-c_1\frac{d}{dx}\right)^nf(x)=0$ for $f(x)$

How to solve this system of ODE: $ u'= - \frac{2v}{t^2}$ and $v'=-u $?

Solving $\frac{dy}{dx}=1+(a_mx^m+a_{m-1}x^{m-1}+...+a_0)y^2$

solution to a general integral $\int_0^\infty \frac{\cos(tx)}{x^2+k^2}e^{-sx}dx$

Solving a third order Euler-Cauchy ODE

Simple proof that the Airy function decays faster than any polynomial