# Intro. to Differential Equations

1. Aug 29, 2006

### bioginz

Just Wondering How....

Hey Guys,

I have learned that Mars and Earth closest encounter so far happened August 27... and it is estimated to commence again by year 2287 if im not mistaken.... I am just wondering how the calculations were made employing the principles of Differential Equations? Im really curious 'bout the accuracy or exactness of the date or just the exact year only...

DANDYBOY

2. Dec 4, 2006

### sina_box

hi to everyone
I am a new user and happy to find this forum.so i'm looking for a way to solve these equations by using delphi programming language.i am a physics student and have "use computer in physics" in this course.
thank you

3. Feb 21, 2007

### mrmotobiker

i just found this useful topic to use in my DE class. does anyone know where i could find solutions (the ones located on the first page of this topic)? they are all too old or not available.

4. Apr 5, 2007

### LRJ85

I tink what hawaii meant was to find the solution to the diff. eqn $$3x^2 \frac{d^2y}{dx^2} - x \frac{dy}{dx} + y = 0$$ at the point xo = 0. After looking through the "Series solution of 2nd Order Linear Equations" in thread #47 written by ExtravagantDreams, i realize that the above diff. eqn can be solved easily. The solution will be of the form y = $$\sum_{n=0}^\infty a_n(x - x_0)^n$$.
Since xo = 0, y = $$\sum_{n=0}^\infty {a_n x^n}$$.
y' = $$\sum_{n=0}^\infty {a_n nx^{n-1}}$$.
y'' = $$\sum_{n=0}^\infty {a_n n(n-1)x^{n-2}}$$.
Now, substitute these expressions into the original diff. eqn:
$$3x^2 \sum_{n=0}^\infty {a_n n(n-1)x^{n-2}} - x \sum_{n=0}^\infty {a_n nx^{n-1}} + \sum_{n=0}^\infty {a_n x^n} = 0$$
Factor in the external x terms:
$$\sum_{n=0}^\infty {3a_n n(n-1)x^n} - \sum_{n=0}^\infty {a_n nx^n} + \sum_{n=0}^\infty {a_n x^n} = 0$$
Combining all the terms since they already have the same degree and same starting pt:
$$\sum_{n=0}^\infty {[3n(n-1) - n + 1]a_n x^n} = 0$$
So finally we arrive at 3n² - 4n + 1 = 0 and an = 0. We get 2 values of n, n=1 and 1/3. How do i proceed from here then??

Any good help would be appreciated :)

Last edited: Apr 5, 2007
5. Apr 5, 2007

### LRJ85

This diff. eqn is of the form $$a \frac{d^3x}{dt^3} + b \frac{d^2x}{dt^2} + c \frac{dx}{dt} + d = f(t)$$ where a,b,c and d are numeric constants. The solution to this is the same as that for 2nd order linear diff. eqns with constant coefficients, provided that f(t) = 0.
So we have $$\frac{d^3x}{dt^3} - 2\frac{d^2x}{dt^2} + \frac{dx}{dt} = 0$$.
The 'kernel' or characteristic equation is in fact:
r³ - 2r² + r = 0
r(r²-2r+1) = 0
r(r-1)² = 0
r= 0, 1 (repeated)
The general solution will be $$x = (c_1t + c_2)e^t + c_3$$ where c1, c2 and c3 are constants of integration.

Correct me if i'm wrong as i'm still new to differential equations :)

6. Aug 27, 2008

### roam

Last edited by a moderator: Apr 23, 2017
7. Sep 25, 2008

Hello Sir,
I m a student of high energy particle physics. Sir i need the solution manual of Differential equations by S.Balachandra Rao. S.B.Rao is the professor in a college of Banglore, India. Sir please if u can do me a favor, plz give me the solution manual of this book. I shall be very very thankful to u. U can email me on this id lost_somewhere@live.com.

Thank U.....

8. Oct 7, 2008

What does

$$\frac {d} {dt}[\mu (t)y] = \mu (t) g(t)$$

mean ? You see I don't have a copy of B&D. )

Last edited: Oct 7, 2008
9. Nov 3, 2008

### bobmerhebi

hello, I'm also taking a class on ODE but i have a problem -i use An Intro course in Diff. eq.'s by Zill - that i get a nonsense result here is the eq:

sin3x + 2y(cos3x)^3 = 0 (here ^ is to raise a power.how are u raising powers?)

the last result i get which is nonsense ofcourse is: y^2 = -1/6(cos3x)^2. another result includes tan3x but is still negative.

so y^2 is negative which is impossible. is the result right? I think there's a problem with the D.E. given.

hope u can help. thx

10. Dec 24, 2009

### Erfan

I had to solve a first-order nonlinear ODE which led me to a this equation.how can I find the solution for y?
yey=f(x)

11. Dec 24, 2009

### Astronuc

Staff Emeritus
Where are the derivatives, e.g., y', or differentials?

12. Dec 25, 2009

### HallsofIvy

"Lambert's W function", W(x), is defined as the inverse function to f(x)= xex. Taking the W function of both sides gives y= W(f(x)).

13. Dec 25, 2009

### Erfan

So the question should be solved numerically using the Lambert's W function? I mean that can't we then have a function in the form: y=f(x)? or we can no more go further than the Lambert's W function?

14. Jan 17, 2011

### chwala

Mathematicians,
i need an insight and understanding of asymptotic behaviour as applied to singular cauchy problem....anyone can comment.........
ken chwala BSC MATHS, MSC APPLIED MATHS FINALIST

Last edited by a moderator: May 5, 2017
15. May 7, 2012

### benz31345

good job

16. Jul 3, 2012

### Luccas

Good night,

Last week I begun to study differential equations by my own and first saw ODE's of separable variables. I've learned very well what they are and how to find constant and non-constant solutions. But something extremely trivial is boring me: I can't figure out why some ODE is or is not of separable variable. For example, I know that an ODE of s.v. is an ODE of the type

[; \frac{dx}{dt} = g(t)h(x) ;]​

but I simply cannot say why

[; \frac{dy}{dx}=\frac{y}{x} ;]​

is and ODE of s.v. and why

[; \frac{dy}{dx}=\frac{x+y}{x^2 +1} ;]​

is not.

I know this is very trivial and I am missing something, but I don't know what. Can you help me, please? :-)

[]'s!

Ps.: sorry for my lousy English.