- #1
sara_87
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solve the diffrential equation:
xy' = x(e^(-y/x)) + y
answer:
y = xln|lncx|
problem:
i don't get it
can anyone explain
xy' = x(e^(-y/x)) + y
answer:
y = xln|lncx|
problem:
i don't get it
can anyone explain
That would indeed be my next stepsara_87 said:yeah i get that... but then i don't know what to do... do we substitute y=vx?
It is indeed. In general ln(a)+ln(b)=ln(ab).sara_87 said:lnC + lnx is lnCx yeah?
sara_87 said:ok
no matter what i do I'm not getting that answer! and its not supposed to a hard question!
i get this:
y = x lnCx
No problemsara_87 said:yes yes yes! i see
cheers!
Differential equations are mathematical equations that describe the relationship between a function and its derivatives. They are used to model a wide range of phenomena in various fields such as physics, engineering, economics, and biology.
The main purpose of solving differential equations is to determine the function or functions that satisfy the given equation. This allows us to make predictions and understand the behavior of systems in real-world situations.
There are several types of differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). ODEs involve a single independent variable, while PDEs involve multiple independent variables. SDEs take into account random processes and are commonly used in finance and physics.
There are various techniques used to solve differential equations, including separation of variables, integral transforms, power series, and numerical methods. The choice of technique depends on the type and complexity of the equation.
Differential equations are essential in science because they provide a mathematical framework for understanding and predicting natural phenomena. They are used to model and analyze a wide range of physical systems, from simple pendulums to complex weather patterns.