@tomleslie Thank you for our time and is there any option to convert original ODE Into a set of the first-order ode by using commands and how to plot the final result if the value of epsilon in numerator A and in denominator  =B for different value of  A and B.

sir one more thing how can i apply perturbation method on the same problem?

@Carl Love yes, you are write  the original Equation is 2d order ode. as now i want to calculate the value of both involved constant of integration that is A and C1 by using the given both boudary condition

@vv with due respect we already follow the same procedure to draw these type of graph and we call this graph streamline graph and they have alot sense to us. i just change the basic equation to draw but faceing issue

@acer dear sir please a complete file, actually i want to plot  please have a look on my file

complete.mw

@vv sir please a look on attached file. I need an expression like in attached file......in this file v is also a function of both x and y

Example_Int.mw

@vv sir i already compute  an expression for v which contain both x and y, i need an expression for v to use another place, i do need required its numeric value

@Kitonum sir is there any method put upward arrow or downward arow through command like we put legends?

@Kitonum  Dear sir you did a lot for me i learn too much from you but still have two issues about plotting

1- how to write subscript in legends i am trying by putting Q[1]=0.5 but fail?

2. if the line of the graph are two close and want to observe the behaviour of the graph and need to add a picture of a specific area as a second graph in the same graph how could we do that.. please see the picture

@Kitonum Dear sir thanks alot, now ut is working according to desire. the last thing i am facing that how to change the length of box that contains the legends...when i draw more the two-line e.g 5 line and i need to show 5 legends but the issue i am facing here is that the width of legends box increases and seem not good according to the graph box, i wish i want to adjust the length og legends box according to the graph.

@Kitonum i am trying to show legends inside the box ( on an empty place right corner or left corner)  but could not find any option. The available option is the only bottom, right, left, upward.please help me regarding this

plot([subs(a = 0.1, Q = 0.5, v), subs(a = 0.2, Q = 0.4, v)], x = 1 .. 10, style = pointline, colour = [black, red], symbol = [solidcircle, asterisk], symbolsize = 15, axes = boxed, numpoints = 20, legend = ["a = 0.1, Q = 0.5", "a = 0.2, Q = 0.4", location = righcorner])

@Kitonum  thanks alost sir, how could i mention two value in one  legends e.g for  a=0.1,Q=0.5, a=0.2,Q=0.4, intotal 5 legends want to show

@Kitonum Dear sir thanks i made correct my mistake

@Kitonum Dear sir why it is giving error, where  i am wrong please correct me my way. i am little confused i abpve file

Help_Appr.mw

@acer  if the above procedure has any ambiguity then can you please help me to construct a polynomial for x in term of c for a=0.1 and b=0.4256  

@acer from above expression i am in need of an explicit expression of x in terms of a,b,c which is further used in another expression for numerical computation of c for different value of a and b.