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

I don't get it.

Latex Help

Rules

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.