Homework Answers
Find the complementary function using general method and find
the perticular integral using variation of parameters method..add
them to get the required solution
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3. Find a solution to the following differential equation y" + y = sec3 t 5 t-2. 3. Find a solution to the following differential equation y" + y = sec3 t 5 t-2.
2. (20 points) Find the solution y (t) of the following differential equation: -{ 0t< 4...
2. (20 points) Find the solution y (t) of the following differential equation: -{ 0t< 4 0 y"9y (t) y(0) = 1, /(0) = 0, t 4 3
3- Find the general solution of the given differential equation 3-2) y'' −2y' +y = e^t /(1+t^2)
3- Find the general solution of the given differential equation 3-2) y'' −2y' +y = e^t /(1+t^2)
Find the general solution of the following differential equation: (1) ?′′ + 5?′ + 6? =...
Find the general solution of the following differential
equation: (1) ?′′ + 5?′ + 6? = 2????*?^? (2) ?′′ + 2?′ + ? = ? +
?e^(-t).
(please solve Question No.7 only)
7. (30 points) Find the general solution of the following differential equation: (1) y" + 5y' + 6y = 2etsint (2) y" + 2y + y=t+te-t 8. (10 points) Use the method of variation of parameters to find a particular solution of y" + y = 1/sin (t),...
Find the general solution to the differential equation: y3 y ' = t Find the general...
Find the general solution to the differential equation: y3 y ' =
t
Find the general solution to the differential equation: y3 y'=t
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a...
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a value ofr for which y = et is a solution to the corresponding homogeneous differential equation. (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation. (c) Use Variation of Parameters to find a particular solution to the nonhomogeneous differ- ential equation and then give the general solution to the differential equation.
Find the general solution of the following non-homogeneous differential equation d 2 y dt2 + 2...
Find
the general solution of the following non-homogeneous differential
equation d 2 y dt2 + 2 dy dt + y = sin (2t). (2) Now, let y(t) be
the general solution you find, when happen if we take lim t→+∞
y(t)?
2. Find the general solution of the following non-homogeneous differential equation dy dy sin (2t) (2) 2 +y= dt dt2 Now, let y(t) be the general solution you find, when happen if we take lim y(t)? t-++oo
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0,...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possi...
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .
1.Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .2.Solve the given initial value problem. y'' + 3y' = 0; y(0) = 12, y'(0)= - 27 The solution is y(t) = _______ 3.Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them z"'+z"-21z'-45z = 0 A general solution is z(t) = _______
D.E. (1) y Find the general solution of the differential equation ay - 25 y' +...
D.E.
(1) y Find the general solution of the differential equation ay - 25 y' + 25 y = 0. (2) Find the particular solution of the initial-value problem y .+ y - 2 y = 0; y(O) = 5, y (0) - - 1 (3) Find the general solution of the differential equation - NO OVERLAP! y. - 3 y - y + 3 y = 54 x - 3e 2x (4) Find the general solution of the differential...
2. (20 points) Find the solution y (t) of the following differential equation: -{ 0t< 4 0 y"9y (t) y(0) = 1, /(0) = 0, t 4 3
Find the general solution of the following differential
equation: (1) ?′′ + 5?′ + 6? = 2????*?^? (2) ?′′ + 2?′ + ? = ? +
?e^(-t).
(please solve Question No.7 only)
7. (30 points) Find the general solution of the following differential equation: (1) y" + 5y' + 6y = 2etsint (2) y" + 2y + y=t+te-t 8. (10 points) Use the method of variation of parameters to find a particular solution of y" + y = 1/sin (t),...
Find the general solution to the differential equation: y3 y ' =
t
Find the general solution to the differential equation: y3 y'=t
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a value ofr for which y = et is a solution to the corresponding homogeneous differential equation. (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation. (c) Use Variation of Parameters to find a particular solution to the nonhomogeneous differ- ential equation and then give the general solution to the differential equation.
Find
the general solution of the following non-homogeneous differential
equation d 2 y dt2 + 2 dy dt + y = sin (2t). (2) Now, let y(t) be
the general solution you find, when happen if we take lim t→+∞
y(t)?
2. Find the general solution of the following non-homogeneous differential equation dy dy sin (2t) (2) 2 +y= dt dt2 Now, let y(t) be the general solution you find, when happen if we take lim y(t)? t-++oo
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
D.E.
(1) y Find the general solution of the differential equation ay - 25 y' + 25 y = 0. (2) Find the particular solution of the initial-value problem y .+ y - 2 y = 0; y(O) = 5, y (0) - - 1 (3) Find the general solution of the differential equation - NO OVERLAP! y. - 3 y - y + 3 y = 54 x - 3e 2x (4) Find the general solution of the differential...
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