# Non linear 2nd order ode not able to solve

• varen90
In summary, the conversation discusses an equation involving constants a, b, and k1, as well as conditions for the function u and its derivative u'. The goal is to find an analytical solution, but no solution has been found yet and the suggestion is to use numerical methods for solving integral equations.
varen90
u'u''-k1u=-a*cos(hy)-b
where,u'=du/dy;
and and a,b,k1 are constants
conditions
u(-H)=0;
u'(0)=0;
where 2H is height of the channel where the liquid is flowing
i couldn't find the analytical soln

u'u''-k1u=-a*cos(hy)-b

(u')^2 u'' - k1 uu' =(-a cos(hy) -b)u'

1/3((u')^3)' - k1/2 ((u)^2)' = (-a cos(hy) -b) u'

Integrate both sides wrt y, where the RHS is:
$$\int_{-H}^{y} (-a \cdot cos(hy) -b) u' = (-a \cdot cos(hy) -b) u(y) - \int (ah \cdot sin(hy) u(y)$$

It doesn't look like there's an analytic solution.

You should try solve it by using numerical methods for solving integral equations.

I can't help more than this, sorry.

thx for the input really appreciated

## 1. Why can't we solve Non linear 2nd order ode analytically?

Non linear 2nd order ode (ordinary differential equation) involves derivatives of the dependent variable raised to powers other than 1, making it a non-linear equation. Non-linear equations do not have a general solution like linear equations, making them difficult to solve analytically.

## 2. Is there any way to solve Non linear 2nd order ode?

Yes, there are numerical methods that can be used to approximate the solution to non-linear 2nd order ode. Some commonly used methods include Euler's method, Runge-Kutta method, and Taylor series method.

## 3. How do we know if a Non linear 2nd order ode is solvable?

There is no definitive way to know if a non-linear 2nd order ode is solvable. However, there are some techniques such as the existence and uniqueness theorem that can be used to determine if a solution exists for a given initial value problem.

## 4. Is it possible to transform a Non linear 2nd order ode into a linear equation?

In some cases, it is possible to transform a non-linear 2nd order ode into a linear equation by using a substitution or change of variables. However, this is not always possible and it depends on the specific equation and its form.

## 5. Can we use software to solve Non linear 2nd order ode?

Yes, there are many software programs, such as MATLAB, Mathematica, and Maple, that have built-in functions for solving non-linear 2nd order ode. These programs use numerical methods to approximate the solution, making it easier and more efficient compared to manual calculations.

• Differential Equations
Replies
3
Views
1K
• Differential Equations
Replies
2
Views
2K
• Differential Equations
Replies
3
Views
2K
• Differential Equations
Replies
7
Views
1K
• Differential Equations
Replies
2
Views
2K
• Differential Equations
Replies
1
Views
2K
• Differential Equations
Replies
5
Views
2K
• Differential Equations
Replies
1
Views
2K
• Differential Equations
Replies
7
Views
2K
• Differential Equations
Replies
2
Views
1K