solving differential Equations

At each point on a certain curve, the slope of the curve is

$$3x^2=\frac{\text{d}y}{\text{d}x}$$ .  If the curve contains the point (0,8), then find its equation using separation of variables.

If

Solve the following differential equations:
$$\frac{\text{d}y}{\text{d}x}=e^x$$  for y(0)=1 using Separation of Variables

Solve the following differential equations:
$$\frac{\text{d}y}{\text{d}x}=3y$$  for y(0)=2 and find y when x=1/3 using Laplace Transform

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

Which of the following is the solution to the differential equation $$\frac{dy}{dx}=\frac{x^2}{y}$$  with the initial condition y(3) = -2?

Let $$\frac{dy}{dx}=-0.4y$$ and  $$y=5\$$  when  $$x=0$$  .  

What is the solution for $$y$$  ?

What is the integral of for $$f\left(t\right)=t^3$$  ? between 0 and 1

What is the integral for $$e^{-2t}$$  ? between 0 and 1

What is Laplace Transform for $$\sin\ 2t$$  ?