- #1

jason17349

- 22

- 0

My problem: find the first solution and use it to find the second solution for

x^2*y"-x*y'+(x^2+1)y=0

assuming y=summation from n=0 to infinity for An*x^n+r

substituting and solving gives me r=1 and a general equation: An=A(n-2)/((n+r)*(n+r-2)+1) for n >= 2

plugging r into my general equation gives An=A(n-2)/((n+1)*(n-1)+1) for n >= 2

plugging n into this I get y=A0*x+(1/4)A0*x^3+(1/64)A0*x^5+(1/2304)A0*x^7... this is y1

now y2=y1*v

I'm not entirely sure what to do after this because I'm unable to reduce y1 to a simple summation which is the only way I've seen this problem done before. Or am I going about this the wrong way?

x^2*y"-x*y'+(x^2+1)y=0

assuming y=summation from n=0 to infinity for An*x^n+r

substituting and solving gives me r=1 and a general equation: An=A(n-2)/((n+r)*(n+r-2)+1) for n >= 2

plugging r into my general equation gives An=A(n-2)/((n+1)*(n-1)+1) for n >= 2

plugging n into this I get y=A0*x+(1/4)A0*x^3+(1/64)A0*x^5+(1/2304)A0*x^7... this is y1

now y2=y1*v

I'm not entirely sure what to do after this because I'm unable to reduce y1 to a simple summation which is the only way I've seen this problem done before. Or am I going about this the wrong way?

Last edited: