Combine the nullifier and parameter variation methods to solve the PVI:
3y'' − 6y' + 30y = 15 sin(x) + e^x tan(3x)
y(0) = 0
y' (0) = 1
Combine the nullifier and parameter variation methods to solve the PVI: 3y'' − 6y' + 30y...
I Discuss how the methods of undetermined coefficients and variation of parameter can be combined to solve the given differential equation. Carry out your ideas. (i) 3y"-6y'+30y-15 sin x + e* tan 3x Page 1 of 4
Solve 5 please 5.7 Exercises In Exercises 1-6 use variation of parameters to find a particular solution. 1. y" +9y = tan 3x 2. y' + 4y = sin 2x sec2 2x 3. y" – 3y' + 2y = 4 4. j" – 2y + 2y = 3e* sec x 1+e-x 4e-x 5. y" – 2y' + y = 14x3/2e* 6. y" - y = 1-e-2x
Consider the differential equation 2y"' + 167" + 30y' = tan(x) Note that y = 1, y = e-3x, and y = e-5x are solutions of the complementary equation. Now consider using variation of parameters. Set up the expression for u,' in determinant form.
Solve Utilizing Laplace Transformations: 3y" + 3y' + 6y = 3e^(-t) * sin2t with initial conditions y(0) = 1 and y'(0) = -1
A) Find the solution of the given 2nd order Homogenous ODE using undetermined coefficient 1) y"-10y, + 25y-30x + 3 4 3) y"- 16y - 2e4x 4) y" + 2y'ysin x + 3 cos 2x B) Find the solution of the given 2nd order Homogenous ODE using variation parameter 1) y" + y sec θ tan θ 1+e 3) 3y''-6y' + 6y = ex secx x+1 A) Find the solution of the given 2nd order Homogenous ODE using undetermined coefficient...
Question 12,15, and 18 Solve differential equation by variation of parameters er 12. y"-2y' + y = 1 + x? 13. y" + 3y' + 2y = sin ex 14. y" 2y 15. y" + 2y, + y = e-t In t
3. Using undetermined coefficients / annihilator or variation of parameter and Cauchy to solve the following: (40 pts) a) 3y"- y"+ 2y'-9y = 130e2+ - 18x² +5 (10 pts)
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHECK YOUR RESULTS. (USE MATRICE FUNCTIONS, PRESS F2. AND THEN PRESS CTRL+SHIFT+ENTER) 3IF Y-SINC) EXPOO. INTEGRATE Y FROM X-0 Tox-1. COMPARE WITH REAL VALUE IF DX-0 a) INT b) INT ,IF DX- 005 REAL VALUE 3) Plot sin x letting maco c/ Prepave hese cuves 4) SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY INVERSE METHOD 3 X+3Z-13 2X +5 Y-2Z-2 3 X+6Y+2Z-3 Z-...
Please use ONLY the variation of parameters method if possible. Thank you! 1. Solve the following differential equations using the method of variation of pa- rameters (for first order equations), or any other acceptable method: cos x + (sin x) y = 1 Ans: y = sin c +C cosx. (b) (x+1) 7 + (x + 2) y = 2xe-* Ans: (x+1)e’y = 22 + C. 2 + (3x + 1) y = e-32 Ans: y = e-3x + Cx-1e-3r.
Use variation of parameters to solve the given nonhomogeneous system. = 4x - - 4y + 7 dx dt dy dt = 3x - 3y - 1 (x(t), y(t)) =