e and g differential equations general solutions and uniqe for e (e) y = x +...
Please show solutions. Answer: 1. Find a general solution to the following differential equations: (a) y" + y = 0 (b) y" – 2y' + 264 = 0 (c) 4x²y" – 3y = 0 (d) y" + 4y = 9 sin(t). (e) y" – 6y' + 9y = 6e3x 1. (a) y = ci + c2e- (b) y = cle' cos(5t) + czet sin(5t) (c) y = cit-1/2 + c2t3/2 (d) y = ci cos(2t) + c2 sin(2t) + 3...
Evaluate the general solutions of the following differential equations: y"-2y'+y = ex/x
1. Find general solutions to the following differential systems of equations using dsolve: a. x' = y + t, y' = 2 -x+t b. x'=s-X, y' = -y - 3x, C. X" = x - x - y, y = -x- y - y - s', s" = -95 d. Solve the equations in c. above with the initial conditions x(0) = 1, x'(0) = 0, y(0) = -1, y'(0) = 0, $(0) = 1, s'(0) = 0, and plot...
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
Differential Equations 7. Show that the two solutions y, = e" and y, = e' of y" + 4y' + 3y = 0 are linearly independent. You need not verify that y, and y, are solutions to the DE. Cite any relevant theorem from the text by theorem number and page number.
Find the general/particular solutions of the given differential equations for problems 1a through 10. (32 points/8 points each) 1a. (y +1)dx =y sec x dy subject to y0) = 1 1b. -X 'y= 2.' Inx, x>0 MATERIAL
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
Differential Equations Need help on understanding how to find General Solutions... y' not y^1 thank you!! General Solution of Bernoulli equation
2. (4 points each) Find the particular solutions for the following differential equations. (a) y" – 4y' = 21 (b) y" +9y sec 3t tan 3t
Differential Equations Series Solutions Near a Ordinary Point find the power series in x for the general solution (1+x^2)y"+2xy-2y=0