Question

Find the particular integral of the differential equation

d^{2}y/dx^{2} + 3dy/dx + 2y = e ^{−2x}
(x + 1). show that the answer is yp(x) = −e ^{−2x} ( 1/2
x^{2} + 2x + 2)

Answer #1

-2e^-2x appears in complementary solution since roots of

Characteristic equation are -1,-2

-2e^-2x appears in complementary solution for c=-2

So it is not appears again in yp

Find the
i)particular integral of the following differential equation
d2y/dx2+y=(x+1)sinx
ii)the complete solution of d3y /dx3-
6d2y/dx2 +12 dy/dx-8 y=e2x
(x+1)

Solve the special type second order differential
equation:
x2*d2y/dx^2+x(dy/dx)=1

Find the differential Equation of
xy'-2y+(2x^3)e^-x=0

Find dy/dx and d2y/dx2 for the given parametric curve. For which
values of t is the curve concave upward? x = t3 + 1, y = t2 − t

Given ?=?^(−?) and ?=??^(6?) find the following derivatives as
functions of ?.
dy/dx=
d2y/dx2=

Find dy/dx and d2y/dx2.
x = t2 + 6, y = t2
+ 7t
For which values of t is the curve concave upward?
(Enter your answer using interval notation.)

Differential Equations
(a) By inspection, find a particular solution of
y'' + 2y = 14.
yp(x)
= ______ANSWER HERE______.
(b) By inspection, find a particular solution of
y'' + 2y =
−4x.
yp(x)
= ______ANSWER HERE______
(c) Find a particular solution of y'' +
2y = −4x + 14.
yp(x)
= _____ANSWER HERE_____
(d) Find a particular solution of y'' +
2y = 8x + 7.
yp(x)
= ___ANSWER HERE____.

Obtain the general solution of
x2d2y/dx2 -2x dy/dx
+2y=sin(lnx)

Transform the differential equation x2d2y/
dx2 − xdy/dx − 3y = x 1−n ln(x), x > 0 to
a linear differential equation with constant coefficients. Hence,
find its complete solution using the D-operator method.

Find the solution of the following differential
equation:
(?^3 y/dx^3)-7(d^2 y/dx^2)+10(dy/dx)=e^2x sinx

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