differentiated system of equations with input at one of the variables

Hello, i have an expression which i need to perform derivatives on it so every derivative will be stored as an expression , and then i need to solve a system of equations where every expression equals zero, with x=1 as an input.

i have tried to write down a code,pseudo matlab code to demonstrate. how can i accomplish this solving ?

maybe we could use

******************

    syms y(t) a
eqn = diff(y,t,2) == a*y;
ySol(t) = dsolve(eqn)
***********************

Thanks

sym a,b,c,d,x

y=a*x^3+b*x^2+c*x+d*sin(x)

y_1=diff(y,x)

y_2=diff(y,x,2)

y_3=diff(y,x,3)

x=1

sol = solve(y_1,y_2,y_3)

[fima v]

i have tried the following but its not working

**********

syms a b c d x

f_1=a*x^3+b*x^2+c*x+d;

f_2=3*a*x^2+2*b*x+c;

f_3=6*a*x+2*b;

f_4=6*a;

eqns=[f_1==0,f_2==0,f_3==0,f_4==0,x==1];

vars=[a b c d ];

[sol_a,sol_b,sol_c,sol_d]=solve(eqns,vars);

Answer 1

[Torsten]

syms a b c d 

x=1;

f_1=a*x^3+b*x^2+c*x+d;
f_2=3*a*x^2+2*b*x+c;
f_3=6*a*x+2*b;
f_4=6*a;

eqns=[f_1==0,f_2==0,f_3==0,f_4==0];
vars=[a b c d ];
[sol_a,sol_b,sol_c,sol_d]=solve(eqns,vars);

Best wishes

Torsten.

[fima v]

Thank you very much