3.2 Problems Find general solutions in powers of x of the diferential equa- tions in Problems 1 t...
2a,2b, and 2c 1. Assuming x > 0, find the general solution of the following Euler equa- tions. f) 5x2y" +12xy' +2y = 0 g) 2y"xy 0 h) a2y" - 2xy =0 i) a2y"-ay-n(n + 2)y 0, where n is a positive integer a) x2y"-3ay 4y 0 b) x2y"-5ay +10y 0 c) 6x2y" +7xy - y 0 d) xy"y0 e) x2y"-3ay' +13y 0 2. Find the solution of the following problems. Before doing these prob- lems, you might want to...
Please do 1a 1b 1d thanks Assuming x > 0, find the general solution of the following Euler equa- tions. a) x²y" – 3xy' +4y=0 (b)x²y" – 5xy +10y=0 f) 5x2y" + 12. y' + 2y = 0 g) x²y" + xy = 0 1. Assuming 2 > 0, find the general solution of the following Euler equa- tions. a) " - 3xy' + 4y = 0 b) – 5xy +10g = 0 c) 6x²y" + 7xy' - y =...
Number 11 please. And please explain the final step to your y= equation 10–14 SERIES SOLUTIONS Find a power series solution in powers of x. Show the details. 10. y" - y' + xy = 0 11. y" - y' + x’y = 0 12. (1 - x?)y" - 2xy' + 2y = 0 13. y" + (1 + x2)y = 0 14. y" - 4xy' + (4x2 – 2y = 0 ons
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly ' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
#16 Please. Step By Step explanation would help me understand. Thank you. In Exercises 1-17 find the general solution, given that yı satisfies the complementary equation. As a byproduct, find a fundamental set of solutions of the complementary equation. 1. (2x + 1)y" – 2y' - (2x + 3)y = (2x + 1)2; yı = e-* 2. x?y" + xy' - y = 3. x2y" – xy' + y = x; y1= x 4 22 y = x 1 4....
#14 please i lution of the great the equation. PROBLEMS: Section 3.8 1/2 use the method of variation of parameters Brahim a parimar solution of the given nonhomogeneous equa- The found the general solution of the equation bytes 27+ y = 1 1 - = - y = 5e 14. xy + xy' - 4y = x(x + x) 1,(x) = x2 Y 2(x) = x-2 15. (1 - x)y" + xy' - y = 2(x - 1)2- y(x) =...
(24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y(1) = 0 (Bernoulli equation) 18 1 b) y" – 4y - 12y = 3e St, y (0) = , y'(0) - (Hint: use the method of undetermined coefficients) c) (2xy - 9x) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE) = -1 7
solve 5c 5. (24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y (1) = 0 (Bernoulli equation) 18 b) y" – 4y' – 12y = 3e5, y (0) =- (Hint: use the method of undetermined 7 coefficients) c) (2xy - 9x?) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE)
April 13, 2020 MATH2107- MIDTERM EXAM.I/1 Q.1(40 pts) Find the solutions of the following differential equa- tion W (2xy + 3y?)dx - (2xy + x2)dy = 0. Q.2(60 pts) Given the differential equation (2xy + y)dx + (2y3 – x)dy = 0. (a) Assuming the integration factor of the form u= u(y), de- termine p(y) so as to make the above equation exact. (b) Then, find the solution of the differential equation. Duration of the exam is 40 minutes.
Find general solutions of the differential equations to x. 14. xy ry-уз 15. y +3y 3xe3 16. y 2-2xy y2 18. 2x2y-rly,-: уз 20. xy' +3y 3x-3/2 11. x2ys xy + 3y2 25. 2y + (x +1)y'-3x +3