# How do you solve a Differential equation for beginners

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^

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rock.freak667
Homework Helper
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.

how do you integrate it ? please tell me how

rock.freak667
Homework Helper
$$\int \frac{1}{y}\frac{dy}{dt} dt= \int t^2 dt$$

and this is the same as:

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

Can you integrate this now?

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

And carry on from there.

Whoops, someone beat me.

what are the rules of integrating

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

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

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