there is an error which is not being corrected. Only its taking x as an input variable.

clc
clear
str2sym x 

ans = 

x

str2sym a0

ans = 

str2sym a1

ans = 

str2sym a2

ans = 

str2sym a3

ans = 

y= a0 + a1*x + a2*x^2 + a3*x^3 ;

Unrecognized function or variable 'a0'.

dy = diff(y);
d2y = diff(dy);
gde = collect( d2y-2*x^2*dy+y,x ) ;
cof =coeffs( gde , x ) ;
A2=solve(cof(1),a2);
A3=solve(cof(2),a3);
y= subs ( y , { a2 , a3 } ,{A2 , A3 } ) ;
y= coeffs( y , [ a1 a0 ] ) ;
disp( 'Solution is ' )
disp ( [ ' y=A ( ' , char ( y ( 1 ) ) , ' + . . . ) + B ( ' , char ( y ( 2 ) ) , ' + . . . ) ' ] )

ERROR:

Unrecognized function or variable 'a0'.

Error in series (line 8)

y= a0 + a1*x + a2*x^2 + a3*x^3 ;

Answer 1

[Cris LaPierre]

I don't think you want to use str2sym to declare your symbolic variables. It is used to evaluate string representing symbolic expression. I think you should just use syms.

syms x a0 a1 a2 a3
y= a0 + a1*x + a2*x^2 + a3*x^3 ;
dy = diff(y);
d2y = diff(dy);
gde = collect( d2y-2*x^2*dy+y,x ) ;
cof =coeffs( gde , x ) ;
A2=solve(cof(1),a2);
A3=solve(cof(2),a3);
y= subs ( y , { a2 , a3 } ,{A2 , A3 } ) ;
y= coeffs( y , [ a1 a0 ] ) ;
disp( 'Solution is ' )

Solution is 

disp ( [ ' y=A ( ' , char(y(1)), ' + . . . ) + B ( ' , char(y(2)), ' + . . . ) ' ] )

 y=A ( 1 - x^2/2 + . . . ) + B ( x - x^3/6 + . . . ) 

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