- #1
sara_87
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Homework Statement
Solve the following ODE:
du/dx=u^2+1
Homework Equations
The Attempt at a Solution
I have tried making the substitution:
u^2=v
but this doesn't help.
Any hints will be very much appreciated
Nonlinear nonhomogeneous ODE of the first kind
- Thread starter sara_87
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- Nonhomogeneous Nonlinear Ode
In summary, a nonlinear nonhomogeneous ODE of the first kind is a type of differential equation that is not linear and not homogeneous, and may include non-constant coefficients. It differs from a linear homogeneous ODE in terms of the linearity and constancy of coefficients. The general solution to a nonlinear nonhomogeneous ODE of the first kind includes arbitrary constants and can be found using various methods. Multiple solutions are possible, but may be limited by initial or boundary conditions. Real-life applications include population growth, chemical reactions, electrical circuits, and mathematical modeling.
Solve the following ODE:
du/dx=u^2+1
I have tried making the substitution:
u^2=v
but this doesn't help.
Any hints will be very much appreciated
- #2
I like Serena
Homework Helper
MHB
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Hi sara_87! 
You have what is called a separable first order ODE.
See the first example on this page:
http://en.wikipedia.org/wiki/Separable_ordinary_differential_equation
Divide both sides of your equation by the right hand side and you should be able to integrate both sides.
You have what is called a separable first order ODE.
See the first example on this page:
http://en.wikipedia.org/wiki/Separable_ordinary_differential_equation
Divide both sides of your equation by the right hand side and you should be able to integrate both sides.
Related to Nonlinear nonhomogeneous ODE of the first kind
1. What is a nonlinear nonhomogeneous ODE of the first kind?
A nonlinear nonhomogeneous ODE of the first kind is a type of differential equation that involves variables and their derivatives, where the equation is not linear (meaning the variables are not raised to a power of 1) and the equation is not homogeneous (meaning all terms have the same degree). It can also include non-constant coefficients.
2. How is a nonlinear nonhomogeneous ODE of the first kind different from a linear homogeneous ODE?
In a linear homogeneous ODE, the equation is linear and all terms have the same degree, and the coefficients are constant. In a nonlinear nonhomogeneous ODE of the first kind, the equation is not linear and the coefficients may be non-constant.
3. What is the general solution to a nonlinear nonhomogeneous ODE of the first kind?
The general solution to a nonlinear nonhomogeneous ODE of the first kind is a solution that satisfies the given equation and includes a set of arbitrary constants. It can be found by using various methods such as separation of variables, variation of parameters, or using specific techniques for certain types of nonlinear ODEs.
4. Can a nonlinear nonhomogeneous ODE of the first kind have multiple solutions?
Yes, a nonlinear nonhomogeneous ODE of the first kind can have multiple solutions. This is because the general solution includes arbitrary constants, which means there can be multiple sets of values for the constants that satisfy the equation. However, the number of solutions may be limited by the initial conditions or boundary conditions given for the specific problem.
5. What are some real-life applications of nonlinear nonhomogeneous ODEs of the first kind?
Nonlinear nonhomogeneous ODEs of the first kind have many applications in physics, engineering, and other scientific fields. Some examples include modeling population growth, analyzing chemical reactions, and predicting the behavior of electrical circuits. They are also commonly used in mathematical modeling to describe complex systems and phenomena.
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