Question

Find the solution of the following differential equation:

(?^3 y/dx^3)-7(d^2 y/dx^2)+10(dy/dx)=e^2x sinx

Answer #1

Given,

----------------(1)

First, find the solution to the homogeneous equation.

The auxiliary equation is

Hence the solution of the complementary equation is,

--------------------(2)

where c_{1}, c_{2}, and c_{3} are
constants.

Now we have to find the particular solution.

Using the method of undetermined coefficients, assume the particular solution as

------------(3)

Now y_{p}(x) satisfies equation (1),

Find

Again differentiating we get,

Again differentiating the above equation we get,

Substituting the values of in (1) we get,

Equating the coefficients of like terms of x in both sides we get,

Solving the above equations we get,

Hence from (3),

Hence the solution of the given differential equation (1) is

1) Solve the given differential equation by separation of
variables.
exy
dy/dx = e−y +
e−6x −
y
2) Solve the given differential
equation by separation of variables.
y ln(x) dx/dy = (y+1/x)^2
3) Find an explicit solution of the given initial-value
problem.
dx/dt = 7(x2 + 1), x( π/4)= 1

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

Find the general solution of the given differential equation
(x+!) dy/dx + (x+2)y = 2xe^-x
y = ______
Determine whether there are any transient terms in the general
solution.

Solve the differential equation (5x^4 y^2+ 2xe^y - 2x cos (x^2)) dx
+ (2x^5y + x^2 e^y) dy = 0.

Find the General Solution of the Differential Equation (y' =
dy/dx) of
xy' = 6y+9x5*y2/3
I understand this is done with Bernoullis Equation but I can't seem
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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 given differential equation
y-x(dy/dx)=3-2x2(dy/dx)

Question 11:
What is the general solution of the following homogeneous
second-order differential equation?
d^2y/dx^2 + 10 dy/dx + 25.y =0
(a)
y = e 12.5.x (Ax + B)
(b)
y = e -5.x (Ax + B)
(c)
y = e -10.x (Ax + B)
(d)
y = e +5.x (Ax + B)
Question 12:
What is the general solution of the following homogeneous
second-order differential equation?
Non-integers are expressed to one decimal place.
d^2y/dx^2 − 38.y =0
(a)
y...

Solve the Homogeneous differential equation
(7 y^2 + 1 xy)dx - 1 x^2 dy = 0
(a) A one-parameter family of solution of the equation is y(x)
=
(b) The particular solution of the equation subject to the
initial condition y(1) =1/7.

Solve the first order homogeneous differential equation:
(2x-5y)dx + (4x-y) dy=0

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