The power series solution of the Initial-Value Problem (IVP) (x² + 1)yl + xy + 2xy...
The power series solution of the Initial-Value Problem (IVP) (x² + 1)yl + xy + 2xy = 0 y(0) = 2 is given by y(0) = 3 4 13 325 2 y=2(1 + + :). 2 + + 3 20 6 2 2125 y= 2 + 3x + +. 6 2 4 23 3.25 y = 32 =3(< + + -) +2 (1 + + :) 3 20 6 2 7.23 21.25 y= 2 + x + + + +......
Question 8 3 pts The power series solution of the Initial-Value Problem (IVP) (x2 + 1)yll + xyl + 2xy = 0 y(0) = 2 is given by y (0) = 3 23 3x5 = 2 1 + + ...)+(2-* + + ...) + 3 20 None of them 7x3 21.25 y= 2 + 3x + +... 6 2 4 --- 3(-one -+...) +2(1-**+..) 7274 y= 2 + x + +...
Question 7 3 pts The solution of the Initial-Value Problem (IVP) zy! - 2y = 4(x - 2) y(1) = 4 y (1) = -1 is 1 23 +22 -3 +3 +2.3 -2.0.4 1 Y L 22 - 2.0 + 4 2 None of them 0 4 2.- - 2 + 1 y = 2 Question 8 3 pts The power series solution of the Initial-Value Problem (IVP) (22 +1)yll + xy + 2xy = 0 y(0) = 2 is...
The power series solution of the Initial-Value Problem (IVP) (a + 1 yul + zy + 2ry = 0 (0) = 2 yu(0) = 3 is given by 2175 °y=2+2+ + + 21 +... None of them 23 3 ey=2(1 - ++) (-) …) +2(1-3 +…) y11= = = = y = 32 + 375 20 + + 2 +...
3 pts Question 7 is The solution of the initial-Value Problem (IVPI 38 - 2y = 4(x - 2) v(I) = 4 W(1) = -1 4 +-9 + 1 O 1 +? - 24 0 417 +-+3 None of them o 1 +- 2c + 4 D Question 8 3 pts The power series solution of the initial Value Problem (IVP) (x+1) + xy + 2xy = 0 (0) = 2 (0) = 3 given by None of them 2125...
Question 7 3 pts The solution of the Initial-Value Problem (IVP) x? yll – 2y = 4(x - 2) y(1) = 4 yl(1) = -1 is 1 y = + x3 - 2x + 4 22 None of them 4 y = + x2 23 + 1 2 1 O Y + x2 – 2x + 4 2 O y = *+2-- + x2 - x + 3 23
2. Use the power series method to solve the following initial-value problem: y" + 2xy' + 8y = 0 with y(0) = 3 and y(0) = 0.
Question 1 4 pts To find a power series solution about x = 0 to y + 2xy = 0, which are procedures needed? Apply the Theorem 3 that all coefficients must be O to determine the coefficients an Show x = 0 is an ordinary point. Shift the indices so that the general term in each is a constant times ck and combined these power series as only one series. All of them Write the solution as a power...
solve the initial value problems by a power series (x-2)y’=xy, y(0)=4
Question 8 (10 marks) Solve the following initial value problem by means of a power series about the ordinary point x=0 y" + 3x?y' + xy = 0, y0)=2, y0) - 6 Find the recurrence relation for the coefficients, and also find the first five non-zero terms of the power series solution