Find the orthogonal trajectories of the family of curves which are defined by y=ce^(2x)
Which is the fundamental set for y'''-2y''+y'
If y1=t and y2=e^(-t) then the Wronskian of y1, and y2, W(y1,y2) is
Let y be a function of t. When changing a second order autonomous equation into a first order non-autonomous equation, which procedure best explains the process.
Which of the following could be a fundamental set for a fourth order linear homogenous differential equation?
Let ?(t) be the solution to
y''=6y'+13y=0, y(?)=e^(3?), y'(?)=e^(3?)
Find ?(0)
1
Let ?(t) be the solution to
2y''-2y'-12y=0, y(0)=1, y'(0)=8
Find ?'''(0)
62
Find W(y1, y2), the Wronskian, of y1, and y2 where they are solutions to (cos t)y''+(1/cost)y'+y=0
What form of a solution would you use to solve
y''-6y'+9y=(1+3x^3)e^3x
using undetermined coefficients?
Suppose that y1 is a solution of y''+2y'-y=4 and y2 is a solution of y''+2y'-y=t. Select the second order linear equation for which 3y1-y2 is a solution
3y''+6y'-3y=36-3t
If y1 and y2 are linearly dependent solutions of
t^2y''?2y'+(3+t)y=0,
then W ( y1, y2)(4) =
0
Let ? ( t) be the solution to y''?2y'+5y=0, y(?/2)=0, y'(?/2)=2. Find ?(?/4).
Which of the following equations can you solve using the method of undetermined coefficients?
Which is a fundamental set for the equation 2y'''+3y'?2y'?3y=0?
Suppose that y 1 is a solution of y''+2y'?y=4 and y2 is a solution of y''+2y'?y=t. Select the second order linear equation for which y1?2 is a solution.
Which are equilibrium solutions to the autonomous equation y'=y^3?y^2?2y with their correct stability?
Find the general solution to
y''?6y'+9y=0
Let v=y'. Find the equations for the trajectories of y''+y^3?4y = 0 in the Poincare plane (the y, y' plane).
What form of a solution would you use to solve y''-3y'+2y = x^2 cos(3x) using undetermined coefficients?
Which is a differential equation for the family of curves which are circles through (0,0) and (0,2)?
Let ? ( t) be the solution to 6y''?5y+y= 0, y(0)=4, y'(0)=0. Find ?(1)
Find W(y1, y2, y3), the Wronskian, of y1=x , y2=cosx, and y3=sinx.
x
Use undetermined coefficients to find the general form of the solution for
y''+y'-12y=cost
...
Use undetermined coefficients to find the general form of the solution for
y''+9y'=5t(e^t)+9
where y1=1 , y2=cost and y3=sint form a fundamental set to the homogeneous equation
...
Use variation of parameters to find a solution of
x^3y'''?3x^2y''+6xy'?6y=2x+3
where y1=x , y2=x^2 and y3=x^3 form a fundamental set to the homogeneous equation
...
Use variation of parameters to find a solution of
y'''+y'=tant
where y1=1 , y2=cost and y3=sint form a fundamental set to the homogeneous equation
...
Use reduction of order to find the general form of the solution to
x^2y''+xy'?4y=0
given that y1(x) =x^2 is a solution to the complementary equation.
...
Find the fundamental set for
(2x+1)xy'''-2(2(x^2)-1)y'-4(x+1)y=0
given that y1(x) =1/x satisfies the equation
...