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3. Given the second-order equation y" +3y2y sin 3t a) Perform an a priori analysis and predict wh...
Given that 6e22 and 5e 3T are solutions of a second order linear homogeneous differential equation...
Given that 6e22 and 5e 3T are solutions of a second order linear homogeneous differential equation with constant coefficients, find this differential equation. a) y" – 1ly' + 30y = 0 b) c) d) e) y" + 1ly' + 30y = 0 y" – y' – 6y = 0 y" + 1ly' – 30y = 0 y" + y' - 6y=0 f) None of the above.
4. (a) Find a second order linear equation which has y as two of its solutions....
4. (a) Find a second order linear equation which has y as two of its solutions. 3e2-2e3and y2--7e+ sin(10t) as one of its (b) Find a second order linear equation which has y solutions. (c) Find two second order linear equations (there are infinitely many) which are satisfied by y- Ce (note this function would not be the general solution of either equation, it only represents some of the possible solutions for each).for any constant C.
Find the general solution of the given second-order differential equation. y'' + 10y' + 25y =...
Find the general solution of the given second-order differential equation. y'' + 10y' + 25y = 0 Solve the given differential equation by undetermined coefficients. y'' + 4y = 2 sin 2x Solve the given differential equation by undetermined coefficients. y'' − y' = −10
2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y =...
2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change the above differential equation so that the general solution to the homogeneous equation will become c cos x + C sinx. c) (7 pnts) Solve the second order linear differential equation y" - y = 3e2x by using Variation of Parameters. 5. a) (7 pnts) Determine the general solution to the system...
4. A forced damped harmonic oscillator is modelled by the equation 6 dt2 dt 9ysin(2t) Perform an a-priory analysis, guessing what the behaviour of the solution should be. Find the solution y(t). Chec...
4. A forced damped harmonic oscillator is modelled by the equation 6 dt2 dt 9ysin(2t) Perform an a-priory analysis, guessing what the behaviour of the solution should be. Find the solution y(t). Check the long term behaviour of our oscillator
4. A forced damped harmonic oscillator is modelled by the equation 6 dt2 dt 9ysin(2t) Perform an a-priory analysis, guessing what the behaviour of the solution should be. Find the solution y(t). Check the long term behaviour of our oscillator
3. Consider the following third order linear differential equation: y3y-4 y'-0 (a) Find the general solution....
3. Consider the following third order linear differential equation: y3y-4 y'-0 (a) Find the general solution. (b) Find the solution that satisfies the following initial conditions: y(0)=4, y'(0)-6, y(0)=-14 (c) Find the dominant eigenvalue, and use it to determine the long-term behavior of the solution.
2. Differential equations and direction fields (a) Find the general solution to the differential equation y'...
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...
9. Question Details ZIDIFEQ9 4.3.009.(38 Find the general solution of the given second-order differential equation. y"+...
9. Question Details ZIDIFEQ9 4.3.009.(38 Find the general solution of the given second-order differential equation. y"+ 36y o y(x) 10. Question Details zomEQ9 4.3.015. Find the general solution of the given higher-order differential equation. yx) - 11.Question Details ZIDTEQ9 4.3.029 Solve the given initial-value problem. y" + 36y-o, y(0)-7, yto)--5 ytx)- 12. Question Details ZIMDifTEQ9 4.4 Solve the given differential equation by undetermined coefficients. y"-6y' + 9y # 6x + 5 y(x)- 13. Question Details ZillDiffE Solve the given differential...
Q.3 (Applications of Linear Second Order ODE): Consider the 'equation of motion given by ODE #1+w2r=...
Q.3 (Applications of Linear Second Order ODE): Consider the 'equation of motion given by ODE #1+w2r= Focos() where Fo and wty are constants. Without worrying about those constants, answer the questions (a) (b). (a) Show that the general solution of the given ODE is 2 pts o(t) :- 1+= cos(wt) + sin(wt) + cos(nt). A) Find the values of u and if the initial conditions are (0) and (0) solution is part (a) can be written explicitly as a(e) -...
Q.3 (Applications of Linear Second Order ODE): Consider the 'equation of motion given by ODE d²x...
Q.3 (Applications of Linear Second Order ODE): Consider the 'equation of motion given by ODE d²x 102 +w²x = Focos(yt) where Fo and wty are constants. Without worrying about those constants, answer the questions (a)-(b). (a) Show that the general solution of the given ODE is [2 pts] Fo x(t) == xc + Ip = ci cos(wt) + C2 sin(wt) +- W2 - 92 cos(7t). (b) Find the values of ci and c2 if the initial conditions are x(0) =...
Given that 6e22 and 5e 3T are solutions of a second order linear homogeneous differential equation with constant coefficients, find this differential equation. a) y" – 1ly' + 30y = 0 b) c) d) e) y" + 1ly' + 30y = 0 y" – y' – 6y = 0 y" + 1ly' – 30y = 0 y" + y' - 6y=0 f) None of the above.
4. (a) Find a second order linear equation which has y as two of its solutions. 3e2-2e3and y2--7e+ sin(10t) as one of its (b) Find a second order linear equation which has y solutions. (c) Find two second order linear equations (there are infinitely many) which are satisfied by y- Ce (note this function would not be the general solution of either equation, it only represents some of the possible solutions for each).for any constant C.
2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change the above differential equation so that the general solution to the homogeneous equation will become c cos x + C sinx. c) (7 pnts) Solve the second order linear differential equation y" - y = 3e2x by using Variation of Parameters. 5. a) (7 pnts) Determine the general solution to the system...
4. A forced damped harmonic oscillator is modelled by the equation 6 dt2 dt 9ysin(2t) Perform an a-priory analysis, guessing what the behaviour of the solution should be. Find the solution y(t). Check the long term behaviour of our oscillator
4. A forced damped harmonic oscillator is modelled by the equation 6 dt2 dt 9ysin(2t) Perform an a-priory analysis, guessing what the behaviour of the solution should be. Find the solution y(t). Check the long term behaviour of our oscillator
3. Consider the following third order linear differential equation: y3y-4 y'-0 (a) Find the general solution. (b) Find the solution that satisfies the following initial conditions: y(0)=4, y'(0)-6, y(0)=-14 (c) Find the dominant eigenvalue, and use it to determine the long-term behavior of the solution.
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...
9. Question Details ZIDIFEQ9 4.3.009.(38 Find the general solution of the given second-order differential equation. y"+ 36y o y(x) 10. Question Details zomEQ9 4.3.015. Find the general solution of the given higher-order differential equation. yx) - 11.Question Details ZIDTEQ9 4.3.029 Solve the given initial-value problem. y" + 36y-o, y(0)-7, yto)--5 ytx)- 12. Question Details ZIMDifTEQ9 4.4 Solve the given differential equation by undetermined coefficients. y"-6y' + 9y # 6x + 5 y(x)- 13. Question Details ZillDiffE Solve the given differential...
Q.3 (Applications of Linear Second Order ODE): Consider the 'equation of motion given by ODE #1+w2r= Focos() where Fo and wty are constants. Without worrying about those constants, answer the questions (a) (b). (a) Show that the general solution of the given ODE is 2 pts o(t) :- 1+= cos(wt) + sin(wt) + cos(nt). A) Find the values of u and if the initial conditions are (0) and (0) solution is part (a) can be written explicitly as a(e) -...
Q.3 (Applications of Linear Second Order ODE): Consider the 'equation of motion given by ODE d²x 102 +w²x = Focos(yt) where Fo and wty are constants. Without worrying about those constants, answer the questions (a)-(b). (a) Show that the general solution of the given ODE is [2 pts] Fo x(t) == xc + Ip = ci cos(wt) + C2 sin(wt) +- W2 - 92 cos(7t). (b) Find the values of ci and c2 if the initial conditions are x(0) =...
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