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Obtain the general solution to the following linear system of 1st order ODE. (1)-(:))
First-Order ODE (a) .Find the general solution of the following ODE: (b). Find the general...
First-Order ODE
(a) .Find the general solution of the following ODE:
(b). Find the general solution (for x > 0) of the ODE :
Hint: try the change of variables u ≜ x, v ≜ y/x.
(c). Find the solution to the ODE
that satisfies y(2) = 15.
Hint: Try separation of variables. For integration,
try partial fraction decomposition.
2Ꮖy 2 Ꭸ , . + <+5 12 , fi - z - ,fix = zu y' = y2...
What is the general intuition behind picking a PARTICULAR solution to a second-order, linear, non-homogenous, ODE...
What is the general intuition behind picking a PARTICULAR solution to a second-order, linear, non-homogenous, ODE y′′+p(t)y′+q(t)y=g(t) instead of following the rules for example when seeing an exponential you know the guess has to include an exponential? P.S I heard the intuition follow somehow checking your guess with the ODE on the left side of the equation and its derivatives before actually applying it, but how?
2. (8 points) Solve the linear, 1st order ODE with initial value: dy dr 3. (7...
2. (8 points) Solve the linear, 1st order ODE with initial value: dy dr 3. (7 points) Find all critical points and the phase portrait of the autonomous Ist order ODE dy dr -5y+4 Classify each critical point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves in the regions in the ry plane separated by equilibrium solutions. dy dx (S points) Solve the Bernoulli equation:-(- 31-1 7. (8 points) Solve the ODE by variation of parameters: -4y+4y (+...
4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b...
any help on these two questions please??
4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b) Find the general real solution of the linear ODE x(t)-Ax(t) + b(t). (c) Solve the initial value problem x(t) = A2(t) + b(t), x(0) = (-2,0,2)T 4.5: Determine the general solution of the ODE x"(t)-x"(t)-r(t) + x(t) = t cost.
4.4: Let 1 0 1 and b(t)- -1 1 0...
just focus on A,B,D 1. Homogeneous ODE Find a general solution of the linear non-constant coefficient,...
just focus on A,B,D
1. Homogeneous ODE Find a general solution of the linear non-constant coefficient, homogeneous ODE for y(x) x3y'" – 3xy" + (6 – x2)xy' – (6 – x?)y = 0 as follows. a) You are given that yı(x) = x is a solution to the above homogeneous ODE. Confirm (by substitution) that this is the case. b) Apply reduction of order to find the remaining two solutions, then state the general solution. (Hint: The substitution y2(x) =...
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) -...
Consider the following second-order ODE representing a spring-mass-damper system for zero initial...
Consider the following second-order ODE representing a spring-mass-damper system for zero initial conditions (forced response): where u is the Unit Step Function (of magnitude 1 a. Use MATLAB to obtain an analytical solution x() for the differential equation, using the Laplace Transforms approach (do not use DSOLVE). Obtain the analytical expression for ao. Also obtain a plot of x() (for a simulation of 14 seconds) b. Obtain the Transfer Function representation for the system. c. Use MATLAB to obtain the...
II) Find the general solution of the following ODE of the 2nd order using the method...
II) Find the general solution of the following ODE of the 2nd order using the method of undetermined coefficients (25 points) y"+2y' y 2xsinx
Differential equations. Please answer all parts of the question! 1.Consider the linear second-order ODE +2y 0....
Differential equations. Please answer all parts of the question!
1.Consider the linear second-order ODE +2y 0. (A) What is the "characteristic polynomial"? (B) What is the "characteristic equation"? And what are the roots? (C) What is the general solution to the ODE? 2.Find the general solution to 324u-y
Need help with all of it Problem 2: Consider the 1st order ODE ry + (2.+...
Need help with all of it
Problem 2: Consider the 1st order ODE ry + (2.+ 3y2 – 20y = 0. (2) As we discussed in class, this ODE isn't linear, exact, or separable. We will now develop a method to solve an ODE like this. Consider the more general case given by the ODE M(2,4) + N(2,4)} = 0 as in our situation, assume this ODE isn't linear, separable, or exact. Our goal will be to find a function...
First-Order ODE
(a) .Find the general solution of the following ODE:
(b). Find the general solution (for x > 0) of the ODE :
Hint: try the change of variables u ≜ x, v ≜ y/x.
(c). Find the solution to the ODE
that satisfies y(2) = 15.
Hint: Try separation of variables. For integration,
try partial fraction decomposition.
2Ꮖy 2 Ꭸ , . + <+5 12 , fi - z - ,fix = zu y' = y2...
2. (8 points) Solve the linear, 1st order ODE with initial value: dy dr 3. (7 points) Find all critical points and the phase portrait of the autonomous Ist order ODE dy dr -5y+4 Classify each critical point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves in the regions in the ry plane separated by equilibrium solutions. dy dx (S points) Solve the Bernoulli equation:-(- 31-1 7. (8 points) Solve the ODE by variation of parameters: -4y+4y (+...
any help on these two questions please??
4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b) Find the general real solution of the linear ODE x(t)-Ax(t) + b(t). (c) Solve the initial value problem x(t) = A2(t) + b(t), x(0) = (-2,0,2)T 4.5: Determine the general solution of the ODE x"(t)-x"(t)-r(t) + x(t) = t cost.
4.4: Let 1 0 1 and b(t)- -1 1 0...
just focus on A,B,D
1. Homogeneous ODE Find a general solution of the linear non-constant coefficient, homogeneous ODE for y(x) x3y'" – 3xy" + (6 – x2)xy' – (6 – x?)y = 0 as follows. a) You are given that yı(x) = x is a solution to the above homogeneous ODE. Confirm (by substitution) that this is the case. b) Apply reduction of order to find the remaining two solutions, then state the general solution. (Hint: The substitution y2(x) =...
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) -...
Consider the following second-order ODE representing a spring-mass-damper system for zero initial conditions (forced response): where u is the Unit Step Function (of magnitude 1 a. Use MATLAB to obtain an analytical solution x() for the differential equation, using the Laplace Transforms approach (do not use DSOLVE). Obtain the analytical expression for ao. Also obtain a plot of x() (for a simulation of 14 seconds) b. Obtain the Transfer Function representation for the system. c. Use MATLAB to obtain the...
II) Find the general solution of the following ODE of the 2nd order using the method of undetermined coefficients (25 points) y"+2y' y 2xsinx
Differential equations. Please answer all parts of the question!
1.Consider the linear second-order ODE +2y 0. (A) What is the "characteristic polynomial"? (B) What is the "characteristic equation"? And what are the roots? (C) What is the general solution to the ODE? 2.Find the general solution to 324u-y
Need help with all of it
Problem 2: Consider the 1st order ODE ry + (2.+ 3y2 – 20y = 0. (2) As we discussed in class, this ODE isn't linear, exact, or separable. We will now develop a method to solve an ODE like this. Consider the more general case given by the ODE M(2,4) + N(2,4)} = 0 as in our situation, assume this ODE isn't linear, separable, or exact. Our goal will be to find a function...
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