Homework Answers
An equation in the form with is called a Bernoulli equation and it can be solved...
An equation in the form
with
is called a Bernoulli equation and it can be solved using the
substitution
which transforms the Bernoulli equation into the following first
order linear equation for
:
Given the Bernoulli equation
we have
so
.
We obtain the equation
.
Solving the resulting first order linear equation for
we obtain the general solution (with arbitrary constant
) given by
Then transforming back into the variables
and
and using the initial condition
to find
....
(1 point) The equation 3ry2r 2y2 (*) can be written in the form y f(y/x), ie.,...
(1 point) The equation 3ry2r 2y2 (*) can be written in the form y f(y/x), ie., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable uu(x. Introducing this substitution and using the fact that y' ru' u we can write () as y xu'w = f(u) where f(u) Separating variables we can write the equation in the form da np (n)6 where g(u) = An implicit general solution with...
(1 point) Solve the Bernoulli initial value problem - 2 'y', y(1)=2 For this example we...
(1 point) Solve the Bernoulli initial value problem - 2 'y', y(1)=2 For this example we haven We obtain the equation + given by Solving the resulting first order linear equation for u we obtain the general solution with arbitrary constant Then transforming back into the variables 2 and y and using the initial condition to find C Finally we obtain the explicit solution of the initial value problem as
(1 point) A Bernoulli differential equation is one of the form dy dc + P(x)y= Q(x)y"...
(1 point) A Bernoulli differential equation is one of the form dy dc + P(x)y= Q(x)y" Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-n transforms the Bernoulli equation into the linear equation du dr +(1 – n)P(x)u = (1 - nQ(x). Consider the initial value problem xy + y = 3xy’, y(1) = -8. (a) This differential equation can be written in the form (*)...
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*)...
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*) Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u =y- transforms the Bemoulli equation into the linear equation + (1 - x)P(3)u = (1 - x)^(x). Consider the initial value problem ry' +y = -3.xy?, y(1) = 2. (a) This differential equation can be written in the form (*) with P(1) =...
A first order linear equation in the form y p(x)y = f(x) can be solved by...
A first order linear equation in the form y p(x)y = f(x) can be solved by finding an integrating factor u(x) = exp c) dx (1) Given the equation y 2xy = 10x find H(x) = (2) Then find an explicit general solution with arbitrary constant C у %3 (3) Then solve the initial value problem with y(0) = 3
A first order linear equation in the form y p(x)y = f(x) can be solved by finding an integrating factor...
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can...
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor μ(x) = exp (1) Given the equation y' + 2y = 2 find μ(x) (2) Then find an explicit general solution with arbitrary constant C p(x) dx (3) Then solve the initial value problem with y(0) 2
(1 point) A first order linear equation in the form y p(x)yf(x) can be solved by...
(1 point) A first order linear equation in the form y p(x)yf(x) can be solved by finding an integrating factor x)expp(x) dx (1) Given the equation y' +2y-8x find u(x) - (2) Then find an explicit general solution with arbitrary constant C. (3) Then solve the initial value problem with y(0) 2 y-
A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn. Observe that, if n=0 or 1,...
A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn. Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y1−n transforms the Bernoulli equation into the linear equation dudx+(1−n)P(x)u=(1−n)Q(x). Use an appropriate substitution to solve the equation y′−5xy=y5x7, and find the solution that satisfies y(1)=1. y(x)=
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can...
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor μ(x) = exp ( (1) Given the equation y, +-= 7x4 find μ(x) (2) Then find an explicit general solution with arbitrary constant C p(x) dx (3) Then solve the initial value problem with y(1) = 2
An equation in the form
with
is called a Bernoulli equation and it can be solved using the
substitution
which transforms the Bernoulli equation into the following first
order linear equation for
:
Given the Bernoulli equation
we have
so
.
We obtain the equation
.
Solving the resulting first order linear equation for
we obtain the general solution (with arbitrary constant
) given by
Then transforming back into the variables
and
and using the initial condition
to find
....
(1 point) The equation 3ry2r 2y2 (*) can be written in the form y f(y/x), ie., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable uu(x. Introducing this substitution and using the fact that y' ru' u we can write () as y xu'w = f(u) where f(u) Separating variables we can write the equation in the form da np (n)6 where g(u) = An implicit general solution with...
(1 point) Solve the Bernoulli initial value problem - 2 'y', y(1)=2 For this example we haven We obtain the equation + given by Solving the resulting first order linear equation for u we obtain the general solution with arbitrary constant Then transforming back into the variables 2 and y and using the initial condition to find C Finally we obtain the explicit solution of the initial value problem as
(1 point) A Bernoulli differential equation is one of the form dy dc + P(x)y= Q(x)y" Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-n transforms the Bernoulli equation into the linear equation du dr +(1 – n)P(x)u = (1 - nQ(x). Consider the initial value problem xy + y = 3xy’, y(1) = -8. (a) This differential equation can be written in the form (*)...
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*) Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u =y- transforms the Bemoulli equation into the linear equation + (1 - x)P(3)u = (1 - x)^(x). Consider the initial value problem ry' +y = -3.xy?, y(1) = 2. (a) This differential equation can be written in the form (*) with P(1) =...
A first order linear equation in the form y p(x)y = f(x) can be solved by finding an integrating factor u(x) = exp c) dx (1) Given the equation y 2xy = 10x find H(x) = (2) Then find an explicit general solution with arbitrary constant C у %3 (3) Then solve the initial value problem with y(0) = 3
A first order linear equation in the form y p(x)y = f(x) can be solved by finding an integrating factor...
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor μ(x) = exp (1) Given the equation y' + 2y = 2 find μ(x) (2) Then find an explicit general solution with arbitrary constant C p(x) dx (3) Then solve the initial value problem with y(0) 2
(1 point) A first order linear equation in the form y p(x)yf(x) can be solved by finding an integrating factor x)expp(x) dx (1) Given the equation y' +2y-8x find u(x) - (2) Then find an explicit general solution with arbitrary constant C. (3) Then solve the initial value problem with y(0) 2 y-
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor μ(x) = exp ( (1) Given the equation y, +-= 7x4 find μ(x) (2) Then find an explicit general solution with arbitrary constant C p(x) dx (3) Then solve the initial value problem with y(1) = 2
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