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differential calculus(First order nonlinear DE)

 
 
Reply Tue 26 Aug, 2014 08:44 am
What is the solution of the differential equation of the form dy/dx=-ax+by^2
and dy/dx=-ax-by^2?Provided that the boundary condition y(c)=0 where a,b,c all are the positive real number.
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Type: Question • Score: 1 • Views: 1,117 • Replies: 3
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Voyager
 
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Reply Thu 28 Aug, 2014 05:47 pm
@krishna basnet,
You should go to

http://www.wolframalpha.com/input/?i=dy%2Fdx%3D-ax%2Bby%5E2+++
krishna basnet
 
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Reply Fri 29 Aug, 2014 01:59 am
@Voyager,
I am not clear that either C1 or C1 and J or C1J both are constant here.please can you clear about constant terms used more properly.

Further more can you provide hits for me for the solution of differential equation

dy/dx=(-cy^2+e/x^2)/(ay-(by/x^2)-f)
here a,b,c,f,e all are real number.
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krishna basnet
 
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Reply Fri 29 Aug, 2014 02:50 am
@Voyager,
Furthermore,in physical sense,I clear you that when x=0, y becomes maximum and have to give certain value.But when we put x=0 in this solution , y=0+0/0 and this become unexpected.so can you have any other possible solution.

If you convert this into second order,then it becomes:
d/dx(dy/dx)-2bydy/dx+a=0
and if we slove the differential equation in homogeneous form then two possible solution be y=-b/x and y=-tan bx.Then if we try to find the general solution for non homogeneous form,then integration appears become unsolved.Can you you slove this type of integral terms?,if you have time please try to observe the solution of this differential equation in this way.If you provide me,any idea for this integration,then result obtained may be interpreted in physiological sense also.So I hopely requested you for this.
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