Find a general solution to the given homogeneous equation. (D+1)?(0-9)º(D+3)(D+ 1) (D? + 49) [y] =...
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t 2x' + y' - 8x - 9y = e-t x' +y' +9x + 4y = et Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. O A. X(t)= C1 e 7t + Cze - 7t + 58 e-t- et O B. X(t) = Cy cos (7t) + C2 sin (7t) OC. x()=C7 e...
The general solution of y(1) – 5y" – 36y = 0) is: (a) y = Cicos 3x + C2 sin 3x + C3e2x + C4e-20 (b) y=Ci cos 3x + C2 sin 3x + C3 cos 2x + C4 sin 2.0 (e) y=Cicos 2x + C2 sin 2x + C3e3x + Cae-31 (d) y=Cicos 2x + C2 sin 2x + C3e3x + Caxe3r (e) None of the above.
dx -7x +y = 0 dt2 Use the elimination method to find a general solution to the given system. dy 7x +- dt2 -7y =e4t 14t 14t OB 14 *(t) =- 32 * +CZ+Czt-Czev 14t-Cye VIA | y(t) = 32 e*+G+Ct+C;evT+t+C;€ VTt X(t) =- 32 24t+C+Cqt-cze +C+Ct-Cev14t-ce-V14 32 24t+c+66+ca e4t+cq+Czt-Czeviat 24++C(zt+Cze/14t+Cge114t X(t) =- 3244t+CZ+C2t+Cze/14t-ce-V14t t) = 32 24t+c4+C2t+cze +C42-714 x(t) = 32@4t+cq+Czt-Czev14t-Ge-V14 Ky(t) = 2 + + 24t+cq+c2t+Cge/14t-Ce-V14 +ce V140 *+C40-V14t 7 X(t) =- 32 9 y(t) = 32 Ос...
QUESTION 10 d x dt2 -7x + y = 0 Use the elimination method to find a general solution to the given system. dy 7x + dt? -7y=e4t x(t) OA y(t) = x(t) ов. y(t) = 1 32 x(t) 32e4t+CZ+Czt-Cze 14t-ce-V14t 32@4t+C+c2t+Czevz4t-cze Ce-/141 32 @4t+CZ+Czt+Czev14t+Ce=V14t 24t+c+C2t+Czev 14t+Cge=V147 *+C+Cat-Czev14t -Ce-/147 €4t+c7+zt+Cze/14t+Cae 24t+C+Czt-Czev 14t-Cae (0) 14+C+CD+C;ev/ |X(t) =- 32°4*+c4+Cat-cz 24t+C+Czt-Cze/14t+cev ********(+6+(30/14-Ge/14 OC 7 - eft, 32 9 32 y(t) = 7 x(t) =- 32 14t - 14t 14t
II. Determine the general solution of the given 2nd order linear homogeneous equation. 1. y" - 2y' + 3y = 0 (ans. y = ci e' cos V2 x + C2 e* sin V2 x) 2. y" + y' - 2y = 0 (ans. y = C1 ex + C2 e -2x) 3. y" + 6y' + 9y = 0 (ans. y = C1 e 3x + c2x e-3x) 4. Y" + 4y = 0, y(t) = 0, y'(T) =...
Find the general solution of y” + 4y' + 5y = 0. Select one: • a. y = {-2x (cos(x) + sin(x)) b. y = e-24 (A cos(x) + B sin(x)) c.y = Cje-2x (cos(x) + sin(x)) O d. y = e*(A cos(2x) + B sin(2x))
6. [0/2 points) DETAILS PREVIOUS ANSWERS Find the general (real) solution of the differential equation: y"- 2y'- 15y=-51 sin(3 x) -3x | Ae 5x + Be 34 y(x) = 8.5 + -cos(3x) * 17 51 14 sin(3x) - - Find the unique solution that satisfies the initial conditions: Y(0) = 2.5 and y'(o)=37 y(x) = 7. [-12 Points) DETAILS Find the general (real) solution of the differential equation: y" + 4y' + 4y=64 cos(2x) y(x) = Find the unique solution...
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...
3. Find the general solution of the differential equation y” + 2y' + y = 0 (a) y=ce' +c,e* (b) y= ce" + xe * (c) y = cxe* +c,e* (d) y= ce* +C,xe" (e) y=ce?* +c,e-2 (f) y= c,e + ,xe” (g) y=cxe?* +cze 2 (h) y= c,e + ,xe 21
find the general solution of the differential equation by using the system of linear equation. please need to be solve by differential equation expert. d^2x/dt^2+x+4dy/dt-4y=4e^t , dx/dt-x+dy/dt+9y=0 Its answer will look lile that: x(t)= c1 e^-2t (2sin(t)+cos(t))+ c2 e^-2t (4e^t-3sin(t)-4cos(t))+ 20 c3 e^-2t(e^t-sin(t)-cos(t))+2 e^t, y(t)= c1 e^-2t sin(t)+ c2 e^-2t(e^t-2sin(t)-cos(t))+ c3 e^-2t(5e^t-12sin(t)-4cos(t))