I have a condition delta(k-r-1);k and  r are integers;

if k-r-1=0,then delta(k-r-1)=1;

if k-r-1 not equal to 0,then delta(k-r-1)=0;

How to write this in if statement?

DE:=f'''(x)+f''(x)(cos(alpha)x+sin(alpha)f(x))/2=0;

ics:=f(0)=0,f'(0)=1,f'(x)=0 for x tends to infinity;

How to solve this DE im RK methods?

I have a equation f(x) = 0.8680555556e-1*x*(3.262720*x^5*n[2]-.63360*x^5*n[1]^2+2.69184*x^5*n[1]-.480*x^3*n[1]^2+2.5920*x^3*n[2]+5.760*n[1]*x+1.920*n[2]*x^2+0.96e-1*x^4*n[1]^3+3.04320*x^4*n[2]-.5280*x^4*n[1]^2-0.32e-1*x^5*n[1]^4+.2976*x^5*n[1]^3-.1184*x^5*n[2]^2+.5376*x^5*n[3]-0.576e-1*x^4*n[1]+.576*x^4*n[3]-6.3360*x^3-6.96960*x^4-7.349760*x^5+11.520-.192*x^5*n[1]*n[3]-.7104*x^4*n[1]*n[2]+.2528*x^5*n[1]^2*n[2]-1.81824*x^5*n[1]*n[2])

with condition  f(0)=0,f'(0)=1;

How to solve this equation and how to find unknown parameters n[1],n[2],n[3]?

I have  sum((r+1)*(r+2)*(r+3)*(r+4)*F(r+4)*(k-r+1)*F(k-r+1), r = 0 .. k) =c (constant); 

outputs: for k=0,1,2,...

                        24 F(4) F(1) = c
                48 F(4) F(2) + 120 F(5) F(1) = c
        72 F(4) F(3) + 240 F(5) F(2) + 360 F(6) F(1) = c....

but I  need the alternate form

F(4)=c/24*F(1),

F(5)=(c-48F(4)F(2))/120*F(1),

F(6)=(c-72*F(4)*F(3)-240*F(5)*F(2))/360*F(1).....

How to change this?

How to write this equation in maple?

g(k-r-1);

conditions:=

1.r from 0 to k, 

2.g(0)=1;

3.g(n)=0, where n not equal to 0.