- Consider The Variable Coefficient Linear Ode Y P X Y G X Y 0 Where P X And Qx Are Polynomials Subsitituting The 1 (60.58 KiB) Viewed 35 times
Consider the variable-coefficient linear ODE y" +p(x)y' + g(x)y=0, where p(x) and qx) are polynomials. Subsitituting the
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Consider the variable-coefficient linear ODE y" +p(x)y' + g(x)y=0, where p(x) and qx) are polynomials. Subsitituting the
Consider the variable-coefficient linear ODE y" +p(x)y' + g(x)y=0, where p(x) and qx) are polynomials. Subsitituting the power series y = m=0 Σ αηαη into the ODE gives ~ Ü (m– 1)mamam-2 2Σ тат хт + 5 ат хт = 0. m=2 m=0 m=0 The recurrence relation is am = 2 m-5 m(m+1) am-2 m = 2,3,4,... O am = 2 m-5 (m-1)(m–2) Fam-2, m=2,3,4,... O am+2 2 m-5 am, (m+1)(m+2) m= 0,1,2,... O am+2 2 m-5 am, m(m-1) m=0,1,2,... oam+2 2 m-5 cam, m(m+1) 0,1,2,... 2 m-5 O am = am-22 m(m-1) m = 2,3,4,...
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