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1. (20) For each question, determine the form of y, for the given DE. Do not...
1. (20) For each question, determine the form of y, for the given DE. Do not...
1. (20) For each question, determine the form of y, for the given DE. Do not solve for A,B,C... Write your answer in the box (a) y" - 54 + 6y - 11 cost=0+e? (b) y' - 5'+by = 4x + 3 We = getes Yp c) y" - 58 +6y=-7x %= + eyes (d) - 54 +6y= -720 W = A + geile Yp (y-2y + 2 = 3e sin We = cos + csin Yp
IV. Determine the form for yp but do NOT evaluate the constants. 1. y" - 5y'...
IV. Determine the form for yp but do NOT evaluate the constants. 1. y" - 5y' + 6y = ex cos 2x + e2x(3x + 4) sin x (ans. this is #21(a) in sec. 3.6) 2. y" - 3 y' - 4 y = 3 e2x + 2 sin x - 8eXcos 2x (ans. Yp = Ae2x + B cos x + C sin x + De* cos 2x + E e sin 2x) V. Solve by variation of parameters....
8. Find the solution to the differential equation y"+2y'+y=sinx using the method of undetermined coefficients. 1...
8. Find the solution to the differential equation y"+2y'+y=sinx using the method of undetermined coefficients. 1 COS X (a) y=ce' +ce' + -cosx 2 (b) y = ce' +cxe'+ (c) y = cxe' +cze cos x (d) y= c,e* + c xe" COSX 1 (e) y=ce' + ce + sinx 2 (f) y=ce' + exe* + sin x 2 (g) y=cxe' + e*- sinx 2 (h) y=ce' + cxe' 1 sinx 9. Use the method of undetermined coefficients to find...
#32 U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In...
#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" –...
Determine the form of a particular solution for the differential equation. Do not solve. y" -...
Determine the form of a particular solution for the differential equation. Do not solve. y" - 4y' + 5y = e 7 + t sin 6t - cos 6t The form of a particular solution is yp(t)- (Do not use d, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
Question 1 5 pts What is the order of the DE? Is the DE linear or...
Question 1 5 pts What is the order of the DE? Is the DE linear or nonlinear? 3 54' - (tan x)y= Vx+ +1 (7) 5.22 3rd order; nonlinear 2nd order; nonlinear 2nd order; linear 3rd order; linear LUCSLIUI 5 pts Is the function y=2e-32 - 4e5x a solution to the DE? Y' - 2y - 15y = 0 O No O Yes Question 3 5 pts Solve the separable DE. dy 3.cy + 2y - 15x - 10 dac...
Find a general solution to the given homogeneous equation. (D+1)?(0-9)º(D+3)(D+ 1) (D? + 49) [y] =...
Find a general solution to the given homogeneous equation. (D+1)?(0-9)º(D+3)(D+ 1) (D? + 49) [y] = 0 Choose the correct answer below. - 3x OA y(x) = C, e ** + C2 e 9x + Cze + C4 COS X + Cs sin x + Cocos 7x + C7 sin 7x OB. y(x) = C, e* + Cze - 9x + C3 e 3x + Ce cos x+Cs sin x+Cg cos 7x+ Cy sin 7x Oc. y(x) = C, e...
help with questions number 4 and 5 only sorry I cropped it Section 4.5 - Method...
help with questions number 4 and 5 only
sorry I cropped it
Section 4.5 - Method of undetermined coefficients, annihilator approach Solve the following using the method of undetermined coefficients, obtain the general solution y = yet Yp! 1. y" – 8y' – 48y = x2 + 6 2. y" – 6y' = sin (2x) 3. y' + 9y = xe6x Section 4.5 - Method of undetermined coefficients, annihilator approach Solve the following using the method of undetermined coefficients, obtain...
solve number 2 for me pls. Step (1) "Rules for Guessing": 1. If y(x) = ek...
solve number 2 for me pls.
Step (1) "Rules for Guessing": 1. If y(x) = ek *. guess that yp(I) = Acts then find A 2. If g(x) = sin(kx), guess that y(x) = A cos(kt) + B sin(kt) then find A and B 3. If g(x) = cos(kx), guess that yp(x) = A cos(kt) + B sin(kt) then find A and B 4. If g(x) is a polyonomial of degree n, guess that ypa) Ao + AX + A₂x²...
As a specific example we consider the non-homogeneous problem y" +9y' + 18y = 9 sin(32)...
As a specific example we consider the non-homogeneous problem y" +9y' + 18y = 9 sin(32) (1) The general solution of the homogeneous problem (called the complementary solution, yc = ayı + by2 ) is given in terms of a pair of linearly independent solutions, 41, 42. Here a and b are arbitrary constants. Find a fundamental set for y" +9y' + 18y = 0 and enter your results as a comma separated list e^(-3x), e^(-x) BEWARE Notice that the...
1. (20) For each question, determine the form of y, for the given DE. Do not solve for A,B,C... Write your answer in the box (a) y" - 54 + 6y - 11 cost=0+e? (b) y' - 5'+by = 4x + 3 We = getes Yp c) y" - 58 +6y=-7x %= + eyes (d) - 54 +6y= -720 W = A + geile Yp (y-2y + 2 = 3e sin We = cos + csin Yp
IV. Determine the form for yp but do NOT evaluate the constants. 1. y" - 5y' + 6y = ex cos 2x + e2x(3x + 4) sin x (ans. this is #21(a) in sec. 3.6) 2. y" - 3 y' - 4 y = 3 e2x + 2 sin x - 8eXcos 2x (ans. Yp = Ae2x + B cos x + C sin x + De* cos 2x + E e sin 2x) V. Solve by variation of parameters....
8. Find the solution to the differential equation y"+2y'+y=sinx using the method of undetermined coefficients. 1 COS X (a) y=ce' +ce' + -cosx 2 (b) y = ce' +cxe'+ (c) y = cxe' +cze cos x (d) y= c,e* + c xe" COSX 1 (e) y=ce' + ce + sinx 2 (f) y=ce' + exe* + sin x 2 (g) y=cxe' + e*- sinx 2 (h) y=ce' + cxe' 1 sinx 9. Use the method of undetermined coefficients to find...
#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" –...
Determine the form of a particular solution for the differential equation. Do not solve. y" - 4y' + 5y = e 7 + t sin 6t - cos 6t The form of a particular solution is yp(t)- (Do not use d, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
Question 1 5 pts What is the order of the DE? Is the DE linear or nonlinear? 3 54' - (tan x)y= Vx+ +1 (7) 5.22 3rd order; nonlinear 2nd order; nonlinear 2nd order; linear 3rd order; linear LUCSLIUI 5 pts Is the function y=2e-32 - 4e5x a solution to the DE? Y' - 2y - 15y = 0 O No O Yes Question 3 5 pts Solve the separable DE. dy 3.cy + 2y - 15x - 10 dac...
Find a general solution to the given homogeneous equation. (D+1)?(0-9)º(D+3)(D+ 1) (D? + 49) [y] = 0 Choose the correct answer below. - 3x OA y(x) = C, e ** + C2 e 9x + Cze + C4 COS X + Cs sin x + Cocos 7x + C7 sin 7x OB. y(x) = C, e* + Cze - 9x + C3 e 3x + Ce cos x+Cs sin x+Cg cos 7x+ Cy sin 7x Oc. y(x) = C, e...
help with questions number 4 and 5 only
sorry I cropped it
Section 4.5 - Method of undetermined coefficients, annihilator approach Solve the following using the method of undetermined coefficients, obtain the general solution y = yet Yp! 1. y" – 8y' – 48y = x2 + 6 2. y" – 6y' = sin (2x) 3. y' + 9y = xe6x Section 4.5 - Method of undetermined coefficients, annihilator approach Solve the following using the method of undetermined coefficients, obtain...
solve number 2 for me pls.
Step (1) "Rules for Guessing": 1. If y(x) = ek *. guess that yp(I) = Acts then find A 2. If g(x) = sin(kx), guess that y(x) = A cos(kt) + B sin(kt) then find A and B 3. If g(x) = cos(kx), guess that yp(x) = A cos(kt) + B sin(kt) then find A and B 4. If g(x) is a polyonomial of degree n, guess that ypa) Ao + AX + A₂x²...
As a specific example we consider the non-homogeneous problem y" +9y' + 18y = 9 sin(32) (1) The general solution of the homogeneous problem (called the complementary solution, yc = ayı + by2 ) is given in terms of a pair of linearly independent solutions, 41, 42. Here a and b are arbitrary constants. Find a fundamental set for y" +9y' + 18y = 0 and enter your results as a comma separated list e^(-3x), e^(-x) BEWARE Notice that the...
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