Solve the given differential equation by separation of variables. (dy)/(dx)=(x^2 y^2)/(1+x)

Find $\frac{dw}{dt}$ using the appropriate Chain Rule. Evaluate $\frac{dw}{dt}$ at the given value of t. Function: $w=x\sin y,x=e^t,y=\pi -t$ Value: $t=0$

Let N be a positive integer. Find all real numbers a such that the differential equation ${\displaystyle \frac{d^{2}y}{d{x}^2}-4a\frac{dy}{dx}+3y=0}$ has a nontrivial solution satisfying the conditions ${\displaystyle y\left(0\right)=0}$ and ${\displaystyle y\left(2N\pi \right)=0}$

What is the surface area of the solid created by revolving
$f(x)=2x^2+3,x\in [1,4]$ around the x axis?

How to determine that this series is conditionally convergent?
$\sum _{n=1}^{\mathrm{\infty }}{\int }_n^{n+1}\frac{\sin \pi x}{x^p+1}\mathrm{d}x,0<p\le 1$

Find the point at which the line intersects the given plane. $x=3-t,y=2+t,z=5t;x-y+2z=9$

I am confused on the following series:
${\displaystyle \sum _{n=1}\frac{1}{n(n+1)}=1}$

Write the equation of the line tangent to ${\displaystyle f\left(x\right)=\tan x+3}$ at ${\displaystyle (\frac{\pi }{4}.4)}$