doraemonpaul
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### Answers (692)

 18 Particular solution to a Riccati equation $y' = 1 + 2y + xy^2$ 13 Finding the Derivative of |x| using the Limit Definition 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 $I=\int_{0}^{1}\sqrt{1-W^2(x)}dx$

### Reputation (9,262)

 -2 $f(x)=f(x+1)$ and $f(-1/x)=f(x)$ +10 Differential Equation $y^2\frac{dy}{dx}+2xy=e^y$ +20 question on separable differential equations +10 Integrate $\int_{-\infty}^\infty \exp (a t^3 + b t^2 + c t) \mathrm{d}t,\;\;(a,c)\in\mathbb{I}, \; \; \Re(b)\le0$

### Questions (33)

 7 About the great result of $\int\underbrace{x^{x^{\cdot^{\cdot^x}}}}_m~dx$ 7 $\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ 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 About fractional differentiation under the integral sign 5 How to solve the nonlinear higher-order PDEs with overdetermined quantities of conditions whose their most-general solutions are known?

### Tags (128)

 270 pde × 360 22 laplace-transform × 37 230 differential-equations × 259 21 indefinite-integrals × 22 90 calculus × 76 21 limits × 4 73 integration × 55 18 recurrence-relations × 23 36 definite-integrals × 24 18 derivatives × 6

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