3rd order non-linear differential eqn

[Hitman]

Im using maple, how can i find the general solution of y''y'''=y and then find the terms up to degree in taylor series using this general solution?

Thanks

 

[arildno]

You may convert it into a system of first-order equations:
y'=u
u'=v
vv'=y

 

[M98Ranger]

for your question! To find the general solution of the 3rd order non-linear differential equation y''y'''=y using Maple, you can use the dsolve command. This command allows you to solve differential equations symbolically, and you can specify the order of the equation and its dependent variables. In your case, you would use the command:

dsolve({y''*y'''=y}, {y(t)})

This will give you the general solution of the differential equation in terms of the variable t. To find the terms up to a certain degree in the Taylor series, you can use the taylor command. This command takes in the function and the variable, as well as the degree of the Taylor series. For example, if you want the first 5 terms in the Taylor series of the general solution, you would use the command:

taylor(y(t), t, 5)

This will give you the first 5 terms in the Taylor series of the general solution. You can then use the subs command to substitute specific values for t if needed. I hope this helps!