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How can I solve this equation using SageMath?

asked 2023-10-20 20:55:45 +0200

stonefaceq gravatar image

updated 2024-04-19 08:24:21 +0200

FrédéricC gravatar image
#general solution
y = function('y')(x)
de = diff(y,x)*(4*x+2*y-3) - 2*x-y-1
solution = desolve(de, y)
solution.show()

#Cauchi problem solution
y=function('y')(x)
de = diff(y,x)*(4*x+2*y-3) - 2*x-y-1
solution=desolve(de,y,ics=[-2,1])
solution.show()
solution1=desolve(de,y,ics=[2,-1])
solution1.show()
solution2=desolve(de,y,ics=[1,1])
solution2.show()
solution3=desolve(de,y,ics=[-1,-1])
solution3.show()

#direction fields
x = var('x')
y = var('y')
f(x,y)= diff(y,x)*(4*x+2*y-3) - 2*x-y-1
p=plot_slope_field(f,(x,-10,10),(y,-10,10), headaxislength=5,
headlength=5,axes_labels=['$x$','$y(x)$'])

#plot of Cauchi problem solution
p+=desolve_rk4(f,y,ics=[-2,1],ivar=x,output='plot',
end_points=[-10,10],thickness=2,rgbcolor=hue(1))
p1=desolve_rk4(f,y,ics=[2,-1],ivar=x,output='plot',
end_points=[-10,10],thickness=2,rgbcolor=hue(0.2))
p2=desolve_rk4(f,y,ics=[1,1],ivar=x,output='plot',
end_points=[-10,10],thickness=2,rgbcolor=hue(0.5))
p3=desolve_rk4(f,y,ics=[-1,-1],ivar=x,output='plot',
end_points=[-10,10],thickness=2,rgbcolor=hue(0.3))
show(p+p1+p2+p3,xmin=-10,xmax=10,ymin=-10,ymax=10)
_____
NotImplementedError: Maxima was unable to solve this ODE. Consider to set option contrib_ode to True.

Here I want to find a solution for a differential equation, solve Cauchi problem and show direction fields. However, Sage can not solve it. It returns an error, showed in the code above. It is solved by hand. So, what can I possibly do?

Equation itself looks like this: (2x+y+1)dx - (4x+2y-3)dy = 0

Thank you

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answered 2023-10-20 22:21:19 +0200

azerbajdzan gravatar image

The error tells you to set option... when done the equation is solved.

y = function('y')(x)
de = diff(y,x)*(4*x+2*y-3) - 2*x-y-1
solution = desolve(de, y,contrib_ode=True)
solution

[-1/5*(4*x + 2*y(x) - 3)*(log(1/(4*x + 2*y(x) - 3) + 1)/(4*x + 2*y(x) - 3) - log(1/(4*x + 2*y(x) - 3))/(4*x + 2*y(x) - 3) - 1) == _C + x]
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Asked: 2023-10-20 20:55:45 +0200

Seen: 123 times

Last updated: Oct 20 '23