how to do #8? 1.1.8 Exercises Verifying Solutions Use direct substitution to verify that y(t) is...
3. Given that yı(t) = t, y(t) = t, and yz(t) = are solutions to the homogeneous differential equation corresponding to ty" + t'y" – 2ty' + 2y = 2*, t > 0, use variation of parameters to find its general solution.
PLEASE ANSWER 2C .PLEASE SHOW ALL STEPS AND WRITE NEATLY Question 2 Determine the unique solutions of the following differential equations by using the Laplace transforms: a. y" – 4y = 4 t, subject to y(0) = 0 and y'(0) = -1. (7) b. y" – 4y' - 5y = 28(t - 2), subject to y(0)=-1 and y'(0) = 0. (8) C. y" + 2y' – 3y = e-3(1-2)u(t – 2), subject to y(0) = 1 and y'(0) = 1....
#32 U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
Can you please show number #25, #27 (Please make work readable) 21. y" + 3y" + 3y' + y = 0 22. y" – 6y" + 12y' – 8y = 0 23. y(a) + y + y" =0 24. y(4) – 2y" +y=0 In Problems 1-14 find the general solution of the given second-order differential equation. 1. 4y" + y' = 0 2. y" – 36y = 0 3. y" - y' - 6y = 0 4. y" – 3y'...
just 44 Euler Equations. In each of Problems 40 through 45, use the substitution introduced in Problem 34 in Section 3.3 to solve the given differential equation. 40. ry' - 3ty' + 4y = 0, [>0 41. y"+2ty' +0.25y = 0, t> 0 42. 2t4y" - Sty' + 5y = 0, [>0 43. r?y' + 3ty' + y = 0, [>0 44. 4rºy' - Sty' +9y = 0, >0 45. Ay' + Sty' + 13y = 0, [>0
correct me if wrong Verify by substitution that y is the solution for the differential equation Y' + 4y = 1.4 The solution is y = Cel-4x) + 0.35 Where the initial Condition (IC) is given by: y(x=0) = 2 y = dy +4y=114 Cdx) dx dy +4y= 1.46dx) dy +4(2)=11444 dy +8=1,4dx
In Exercises 5-14, use the addition method to solve each system of equations. (Exercises 5-8 are the same as Exercises 1-4.) 2x+y+z=7 x+y+5z =-10 2x 3y +3z9 118.txx y y 552:1 i3 11(2xx+ 23y +42c:17 1 13.?s- x-2y + z=-4 x+2y + 3z = 4 4x+2y + 2z = 0 16x-4y-3z = 3 6x+3y + 12z = 6 Solve Exercises 15-22 15. Electronics Kirchhoff's law for current states 13 (Note that electu
This is equation 8: full question, which contains y1 ya(t) = n(e) / 102 . Use Equation (8) above or go through the reductio-of-order process to find a second solution 72 of the preceding equation such that {/1,} is a fundamental set of solutions of y" - (1+ y + 4y = 0 on (0,0). Y2 = Y = Solve the initial-value problem y"(t) + 4y'(t) + 13y(t) =0, y(0) = 3, y'(O) = 6. Express you answer in the...
Just #2, 14, 16. Thank you EXERCISE SET 1.2 Practice Exercises In Exercises 1-16, solve and check each linear equation. 1. 7x 5 72 3. 11x - (6x -5) 40 5x (2x 10) 35 6.3x+5=2x+13 8. 13x + 14 = 12x-5 7. 7x 4x + 16 9. 3(r 2) +7 2(x + 5) 10. 2(x 1) +3 - 3(r + 1) 11. 3(x-4)-4(x _ 3) = x + 3-(x-2) 12. 2-(7x +5) 13 3x 13. 16 3(x 1) - (r...
if t < 41 8(t) = 41 if t > 41 Solve the differential equation y(0) = 6, 7(0) = 5 y" +4y = g(t), using Laplace transforms. ift < 41 if t > 411