- #1
shseo0315
- 19
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Homework Statement
(1+x)^2 dy/dx = (1+y)^2
Homework Equations
The Attempt at a Solution
The post I put up a while ago actually turns out to be the one above.
So far I'm not getting the right answer, please help.
shseo0315 said:Thanks.
But on the way, 1/(1+x^2)dx = 1/(1+y^2)dy
if I take an intergral, I get
-1/(x+1) + c = -1/(y+1) + c
This is 1/(x+1) + c = 1/(y+1) right?
The answer states that y = (1+x)/[1+c(1+x)] -1
I don't know how to get there.
Dick said:Right. You never really needed two c's. Just take your expression and use algebra to solve for y.
shseo0315 said:from 1/(x+1) +c = 1/(y+1)
that is y+1+c = x+1 right
y(x) = x+c
this is what I get, but the answer is quite different
which is y = (1+x)/[1+c(1+x)] -1
A differential equation is a mathematical equation that relates one or more functions and their derivatives. It describes how a quantity changes with respect to another quantity.
The main types of differential equations are ordinary differential equations, partial differential equations, and stochastic differential equations. Ordinary differential equations involve only one independent variable, while partial differential equations involve multiple independent variables. Stochastic differential equations involve random variables and are used in modeling systems with uncertainty.
Differential equations have a wide range of applications in various fields such as physics, engineering, economics, biology, and chemistry. They are used to model and analyze systems and phenomena that involve change over time, such as motion, population growth, chemical reactions, and heat transfer.
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Differential equations are important because they provide a powerful tool for describing and predicting the behavior of systems and phenomena. They are also used in developing mathematical models for real-world problems and are essential in many scientific and engineering fields.