How do you solve a Differential equation for beginners

[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^

 

[Google_Spider]

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

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

 

[Google_Spider]

I don't get it.

https://www.physicsforums.com/showthread.php?t=8997"


https://www.physicsforums.com/showthread.php?t=94379"

 

[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.

 

[janemba]

how do you integrate it ? please tell me how

 

[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?

 

[Snazzy]

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

And carry on from there.

Whoops, someone beat me.

 

[janemba]

what are the rules of integrating

 

[Snazzy]

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

 

[janemba]

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

 

[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.