# doraemonpaul

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 14 Particular solution to a Riccati equation $y' = 1 + 2y + xy^2$ 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 Solving 4th-order PDE 7 How find this integral $I=\int_{0}^{1}\sqrt{1-W^2(x)}dx$ 7 Stochastic Heat Equation

# 6,376 Reputation

 +15 Integral in Polar Co-ordinates: Can you help evaluate it? +25 Solving a first order nonlinear PDE +15 Method of characteristics (quasilinear pde- nonlinear transport ) +10 Indefinite integral $\int \left(\frac{\arctan x}{\arctan x - x}\right)^3 \mathrm{dx}$

# 33 Questions

 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 About the great result of $\int\underbrace{x^{x^{\cdot^{\cdot^x}}}}_m~dx$ 5 $\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$ 5 About fractional differentiation under the integral sign 4 How to solve the nonlinear higher-order PDEs with overdetermined quantities of conditions whose their most-general solutions are known?

# 106 Tags

 206 pde × 254 16 indefinite-integrals × 18 152 differential-equations × 167 15 special-functions × 14 61 integration × 43 13 recurrence-relations × 20 56 calculus × 50 13 fourier-analysis × 13 33 definite-integrals × 19 12 laplace-transform × 27

# 5 Accounts

 Mathematics 6,376 rep 11041 Mathematics Educators 240 rep 18 Area 51 171 rep 3 Stack Overflow 101 rep Meta Stack Exchange 101 rep 1