- #1
ELESSAR TELKONT
- 44
- 0
I have two problems and I don't know what they want to tell. Please tell me what do you think
1. We define operator [tex]L[x]=a(t)\ddot{x}+b(t)\dot{x}+c(t)x[/tex] in [tex]C^{2}(I)[/tex] function space. Proof that [tex]\frac{\partial}{\partial\lambda}L[x]=L\left[\frac{\partial x}{\partial\lambda}\right][/tex]. ¿What do you think the lambda is for? I don't understand! We haven't done anything like that in the course.
2.Bessel equation of zero order. Use the Frobenius Method to show that [tex]L[x]=a_{0}\lambda^{2}t^{\lambda}[/tex], with the supposition that the coefficient of [tex]t^{n+\lambda}[/tex] for [tex]n\geq 1[/tex] vanishes and that the root of the indical polinomial is of multiplicity 2, and show that [tex]L\left[\frac{\partial x}{\partial\lambda}\right]=2a_{0}\lambda t^{\lambda}+a_{0}\lambda^{2}t^{\lambda}\ln t[/tex]. ¿What do you think the lambda is for? I have searched in books and internet and I never saw that the Bessel equation of zero order have the form that this problem makes use.
Please help me to decipher what the hell teacher's assistant was thinking when he wrote the homework. It's urgent.
1. We define operator [tex]L[x]=a(t)\ddot{x}+b(t)\dot{x}+c(t)x[/tex] in [tex]C^{2}(I)[/tex] function space. Proof that [tex]\frac{\partial}{\partial\lambda}L[x]=L\left[\frac{\partial x}{\partial\lambda}\right][/tex]. ¿What do you think the lambda is for? I don't understand! We haven't done anything like that in the course.
2.Bessel equation of zero order. Use the Frobenius Method to show that [tex]L[x]=a_{0}\lambda^{2}t^{\lambda}[/tex], with the supposition that the coefficient of [tex]t^{n+\lambda}[/tex] for [tex]n\geq 1[/tex] vanishes and that the root of the indical polinomial is of multiplicity 2, and show that [tex]L\left[\frac{\partial x}{\partial\lambda}\right]=2a_{0}\lambda t^{\lambda}+a_{0}\lambda^{2}t^{\lambda}\ln t[/tex]. ¿What do you think the lambda is for? I have searched in books and internet and I never saw that the Bessel equation of zero order have the form that this problem makes use.
Please help me to decipher what the hell teacher's assistant was thinking when he wrote the homework. It's urgent.