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(1)(1)

(3)(3)

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(2)(2)

restart;ode := diff(w(eta),eta,eta)+(n-1)/eta*diff(w(eta),eta)-diff(w(eta),eta)^2/w(eta)+w(eta)^2;

ode d d2

dη2

w η C

nK1 d

dη w η

ηK

d

dη w η

2

w ηCw η

2

n := 1;n d 1

L0:=1e-3:pp := dsolve({ode, w(L0)=1, D(w)(L0)=0}, numeric):

pp(1);

η = 1., w η = 0.629832160095156,d

dη w η =K0.541924897314378

with(plots):odeplot(pp, [eta^2*w(eta), 1/w(eta)], eta=L0..5, numpoints=1300);pic1:=%:

eta^2*w0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1/w

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(5)(5)

(4)(4)

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display(%, view=[0..2.1,0..20]);

eta^2*w0 0.5 1 1.5 2

1/w

0

5

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20

n := 2;n d 2

L0:=1e-3:pp := dsolve({ode, w(L0)=1, D(w)(L0)=0}, numeric):

pp(1);

η = 1., w η = 0.790125765797306,d

dη w η =K0.351167703945346

odeplot(pp, [eta^2*w(eta), 1/w(eta)], eta=L0..10, numpoints=1300);pic1:=%:

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eta^2*w0 0.5 1 1.5 2

1/w

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display(%, view=[0..2.1,0..20]);

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(6)(6)

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(7)(7)

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eta^2*w0 0.5 1 1.5 2

1/w

0

5

10

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20

n := 3;n d 3

L0:=1e-3:pp := dsolve({ode, w(L0)=1, D(w)(L0)=0}, numeric):

pp(1);

η = 1., w η = 0.853143751531509,d

dη w η =K0.258418593583166

odeplot(pp, [eta^2*w(eta), 1/w(eta)], eta=L0..120, numpoints=1300);pic1:=%:

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eta^2*w0 1 2 3

1/w

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7000

display(%, view=[0..5,0..100]);

eta^2*w0 1 2 3 4 5

1/w

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