# How do you solve a Differential equation for beginners

1. Mar 24, 2008

### janemba

how do you solve a Differential equation ?

for example how do you solve this

d/dt y(t)=t^2 y(t)

step by step help would be appreciated where + w2x = 0 is suppose to be in between d^x and dt^

Last edited: Mar 24, 2008
2. Mar 24, 2008

What are [ U] and [ /U] tags ?

Use [ tex] and [ /tex] for latex. The equation is not visible.

3. Mar 24, 2008

Last edited by a moderator: Apr 23, 2017
4. Mar 24, 2008

### rock.freak667

What you want to solve is
$$\frac{dy}{dt}=t^2y$$
You can rearrange this into
$$\frac{1}{y}\frac{dy}{dt}=t^2$$
You can now integrate both sides with respect to t.

5. Mar 24, 2008

### janemba

how do you integrate it ? please tell me how

6. Mar 24, 2008

### rock.freak667

$$\int \frac{1}{y}\frac{dy}{dt} dt= \int t^2 dt$$

and this is the same as:

$$\int \frac{1}{y}dy= \int t^2 dt$$

Can you integrate this now?

7. Mar 24, 2008

### Snazzy

$$\int \frac{1}{y}dy = \int t^2dt$$

And carry on from there.

Whoops, someone beat me.

8. Mar 24, 2008

### janemba

what are the rules of integrating

9. Mar 24, 2008

### Snazzy

You can look up integration rules on the internet. Integrating is undoing the derivative, ie. finding the antiderivative.

10. Mar 24, 2008

### janemba

wheres the best site to learn it from ? where did you learn it from

11. Mar 24, 2008

### Snazzy

I learned it through a high school calculus course. If you don't know how to integrate, I suggest you ask your professor/teacher.