Use ‘Reduction of Order’ to find a second solution y2 to the
given ODEs:
(a) y′′+2y′+y=0, y1 =xe−x
(b) y′′+9y=0, y1 =sin3x
(c) x2y′′+2xy′−6y=0, y1 =x2
(d) xy′′ +y′ =0, y1 =lnx
Problem 4. From order two to order three:
(a) Find the general solution of y′′′ + 3y′′ + 3y′ + y = 0.
(b) Write a differential equation given that the fundamental system
of solutions is
ex,exsinx, excosx.
(c) Compute the general solution of xy′′′ + y′′ = x2. [Answer: C1x
ln x + C2x + C3 + x4 .]
Find a general solution to the differential equation using the
method of variation of parameters.
y''+ 25y= sec5t
The general solution is y(t)= ___
y''+9y= csc^2(3t)
The general solution is y(t)= ___
1)Find the general solution of the given second-order
differential equation.
y'' − 7y' + 6y = 0
2)Solve the given differential equation by undetermined
coefficients.
y'' + 4y = 6 sin(2x)