doraemonpaul

 40 Finding the Derivative of |x| using the Limit Definition 19 Particular solution to a Riccati equation $y' = 1 + 2y + xy^2$ 10 Solving 4th-order PDE 8 Integral $S_\ell(r) = \int_0^{\pi}\int_{\phi}^{\pi}\frac{(1+ r \cos \psi)^{\ell+1}}{(1+ r \cos \phi)^\ell} \rm d\psi \ \rm d\phi$ 8 Stochastic Heat Equation

### Reputation (13,394)

 +10 Bessel function recursion relation +15 Solve a PDE, modified Heat $u_t+u_{xx}/2 +xu = 0$; Where $u(T,x)=1$. +10 Solving a Non linear ODE +15 Can this be integrated in any way?

### Questions (39)

 8 About the great result of $\int\underbrace{x^{x^{\cdot^{\cdot^x}}}}_m~dx$ 8 $\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$ 7 How to find the general solution of $xy''-(2x+1)y'+x^2y=0$ when we know the general solution of $y''+2y'+xy=0$? 6 Why solving $\dfrac{\partial u}{\partial x}=\dfrac{\partial^2u}{\partial y^2}$ like this is wrong? 5 How to solve the nonlinear higher-order PDEs with overdetermined quantities of conditions whose their most-general solutions are known?

### Tags (170)

 382 ordinary-differential-equations × 469 49 limits × 5 360 pde × 451 43 definite-integrals × 24 142 calculus × 101 42 functional-equations × 60 91 integration × 62 35 laplace-transform × 51 51 derivatives × 11 31 special-functions × 29

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 Mathematics 13,394 rep 31861 Mathematics Educators 300 rep 28 Area 51 171 rep 3 Physics 106 rep 2 Stack Overflow 101 rep