How do you solve a Differential equation for beginners

In summary, differential equations can be solved by rearranging the equation and then integrating both sides. The rules of integration can be found online or learned through a calculus course.
  • #1
janemba
39
0
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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  • #2
What are [ U] and [ /U] tags ?

Use [ tex] and [ /tex] for latex. The equation is not visible.
 
  • #4
What you want to solve is
[tex]\frac{dy}{dt}=t^2y[/tex]
You can rearrange this into
[tex]\frac{1}{y}\frac{dy}{dt}=t^2[/tex]
You can now integrate both sides with respect to t.
 
  • #5
how do you integrate it ? please tell me how
 
  • #6
[tex]\int \frac{1}{y}\frac{dy}{dt} dt= \int t^2 dt[/tex]

and this is the same as:

[tex]\int \frac{1}{y}dy= \int t^2 dt[/tex]

Can you integrate this now?
 
  • #7
[tex]\int \frac{1}{y}dy = \int t^2dt[/tex]

And carry on from there.

Whoops, someone beat me.
 
  • #8
what are the rules of integrating
 
  • #9
You can look up integration rules on the internet. Integrating is undoing the derivative, ie. finding the antiderivative.
 
  • #10
wheres the best site to learn it from ? where did you learn it from
 
  • #11
I learned it through a high school calculus course. If you don't know how to integrate, I suggest you ask your professor/teacher.
 

1. What is a differential equation?

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It is commonly used to model real-world phenomena in fields such as physics, engineering, and economics.

2. How do you solve a differential equation?

There are several methods for solving differential equations, including separation of variables, integrating factors, and using power series. The specific method used depends on the type and complexity of the equation.

3. What does it mean to "solve" a differential equation?

Solving a differential equation means finding a function that satisfies the equation. In other words, it involves finding the unknown function that satisfies the given equation and its initial conditions.

4. Do I need to have a strong math background to solve differential equations?

While a strong math background can certainly be helpful, it is not necessary to solve differential equations. Many introductory differential equations courses assume only basic knowledge of algebra, calculus, and trigonometry.

5. Are there any applications of differential equations in everyday life?

Yes, differential equations are used to model and understand various real-world phenomena, such as population growth, heat transfer, and electrical circuits. They are also used in fields such as finance, medicine, and biology.

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