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Question: What kind of solution is it ?

Question:What kind of solution is it ?

Ahmed111 130 Maple 2022
ode dsolve differential-equations
December 20 2022
1

What kind of solution is it (see (3))? Why is there no solution when I put the initial condition v(0)=C1? Secondly, eq. (2) can be reduced to a first-order differential equation?

> 

restart
> 

interface(showassumed = 0)

declare(v(y))

 (1)
> 

q := v(y)*(diff(diff(diff(v(y), y), y), y))+(2*v(y)-(diff(v(y), y)))*(diff(diff(v(y), y), y))+(diff(v(y), y))*(v(y)^3+v(y)-(diff(v(y), y))) = 0

v(y)*(diff(diff(diff(v(y), y), y), y))+(2*v(y)-(diff(v(y), y)))*(diff(diff(v(y), y), y))+(diff(v(y), y))*(v(y)^3+v(y)-(diff(v(y), y))) = 0

 (2)
> 

dsolve(q)

v(y) = ODESolStruc(_a, [{(diff(diff(_b(_a), _a), _a))*_b(_a)^2+_b(_a)*((diff(_b(_a), _a))^2*_a+_a^3-(diff(_b(_a), _a))*_b(_a)+2*(diff(_b(_a), _a))*_a-_b(_a)+_a)/_a = 0}, {_a = v(y), _b(_a) = diff(v(y), y)}, {y = Int(1/_b(_a), _a)+_C1, v(y) = _a}])

 (3)
> 

NULL
> 

dsolve({q, v(0) = C1})

v(y) = C1

 (4)
> 

NULL

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