1. Determine the form of a particular solution for the following
differential equations. (Do not evaluate the coefficients.)
(a) y'' − y' − 6y = x^2 e^x sin x + (2x^3 − 1)e ^ cos x.
(b) y'' − y' − 6y = (2 − 3x^3 )e^3x .
(c) y'' + 4y' + 4y = x(e^x + e^−x )^2 .
(d) y'' − 2y' + 2y = (x − 1)e^x sin x + x^2 e^−x cos x.
2. Find a...
Determine the reasonable form of the particular solution for
each non homogeneous differential equation. Do not solve it.
a) y''-y'-2y= e^-x+xcos2x+e^xsin2x.
b) D^2[y] +4y =1+x^2+xsin2x.
Set up the appropriate form of the particular solution to each
of the differential equations below, but do NOT determine the
values of the coefficients.
(a) y′′ +10y′ +25y=2e^(5t) +te^(−5t)
b) y′′ +9y=5t^2 +4cos(3t)+6e^(3t)
Find the general solution of the following
differential equations (complementary function
+ particular solution). Find the particular solution by inspection
or by (6.18), (6.23),
or (6.24). Also find a computer solution and reconcile differences
if necessary, noticing
especially whether the particular solution is in simplest form [see
(6.26) and the discussion
after (6.15)].
(D2+2D+17)y = 60e−4x sin 5x
Using the method of undetermined coefficients determine the
exact (only) of a particular solution. Do not evaluate the
coefficients.
y''' + 2y'' + y' = 5e-tsin(t) + 3 +
7te-t
Use method of undetermined coefficients to find a particular
solution of the differential equation ?′′ + 9? = cos3? + 2. Check
that the obtained particular solution satisfies the differential
equation.
For each of the following differential equations, find the
particular solution that satisfies the additional given property
(called an initial condition).
y'y = x + 1
Find a particular solution yp of the following
EQUATIONS using the Method of Undetermined Coefficients. Primes
denote the derivatives with respect to x.
y''-16y=cos h(4x)
y''+36y=12cos(6x)+18sin(6x)
y''+4y'+8y=325e2tcos(5t)
y(5)+6y(4)-y=12
y(5)+2y(3)+2y''=8x2-2
SOLVE ALL ~ do ur besest (:
a) Determine the correct form of the particular solution
y" + y = sin x
b) Solve IVP: y" + y = e^x + x^3; y(0) = 2, y'(0) = 0
c) Solve IVP: y" + y' -2y = x + sin 2x; y(0) = 1, y'(0) = 0
Determine the general solution of the differential equations.
Write out the solution ? explicitly as a function of ?.
(a) 3?^2?^2 ??/?? = 2?−1
(b) 2 ??/?? + 3? = ?^−2? − 5