Consider the differential equation x2y′′+x(1+2N −x)y′+N2y =0, x > 0. ...........(11.7.11) Q.)Determine the Frobenius series solutions when N =0,1,2,3.
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Consider the
x2y′′+x(1+2N −x)y′+N2y =0, x > 0. ...........(11.7.11)
Q.)Determine the Frobenius series solutions when N =0,1,2,3.
As per the question we are given the following 2nd order linear differential equation :
x2y′′ + x(1+2N −x)y′+ N2y = 0
And we have to find its Frobenius series solutions for N = 0, 1, 2, 3
For this we will first solve for the general solution then we will substitute N = 0, 1, 2, 3
Step by step
Solved in 2 steps with 1 images
- 2. Use the Frobenius series to find the solution of in some interval 0 < x < d. 1²y" +1(2+1)y' - 2y = 0Use the procedure in Example 8 in Section 6.2 to find two power series solutions of the given differential equation about the ordinary point x = 0. y' + e'y' – y = 0 1,3 ܐ ܐܨܐ ܀ Oy=1+ Oy, =1+ 2 Oy =1+ 2 ܠܐܕܐܐܨܐ+Oy + + .… and y2 - X - and y, = x + Oy:=1+_x+x + 2 3 and y, = x - +ܐ 4 ܡܐ ܠܨ-xܕx- + y+1-:0 ܕܨܐ y2 X + 13 and y2 = x 6 + ܟܛܚ ܕ - -x- ܕOy -1- o- 3 - .… and y ܐܐܐܐ 4 9 1 24 - 9 1 24 ܐ ܐ ܐ x- + .… 1 16 1x2 + 1x³ + 1 169. The differential equation has a power series solution A) -3 B) -1 C) for some constant real numbers A, B and C. Find the value of C. D) E) 100 1 40 2y" + xy + y = 0 1 20 y = 4-3x+ Ar² + + Bx²¹ +Cx³ +..
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