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)=
Homework Answers
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A Bernoulli differential equation is one of the form
dydx+P(x)y=Q(x)yn.
Observe that, if n=0 or 1,...
(1 point) A Bernoulli differential equation is one of the form dete+ P(x)y= Q(2)y". Observe that,...
(1 point) A Bernoulli differential equation is one of the form dete+ P(x)y= Q(2)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 am + (1 – n)P(x)u = (1 – n)Q(x). Use an appropriate substitution to solve the equation and find the solution that satisfies y(1) = 1. y(x) =
(15 points) A Bernoulli differential equation is one of the form dy dar + P(x)y= Q(x)y"....
(15 points) A Bernoulli differential equation is one of the form dy dar + 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 + (1 - n)P(x) = (1 - nQ(x). dx Use an appropriate substitution to solve the equation xy' +y=2xy? and find the solution that satisfies y(1) = 1.
(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) =...
Fill in the blanks (1 point) A Bernoulli differential equation is one of the form dy...
Fill in the blanks
(1 point) A Bernoulli differential equation is one of the form dy + P()y= Q(Cy" (*) dr 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 dac + (1 - n)P(x)u= (1 - nQ(2). Consider the initial value problem xy' +y= -6xy?, y(1) = -2. (a) This differential equation can be written in the form...
HW 2.4: Problem 3 Previous Problem Problem List Next Problem (1 point) A Bernoulli differential equation...
HW 2.4: Problem 3 Previous Problem Problem List Next Problem (1 point) A Bernoulli differential equation is one of the form + P(x)y -- Q(x)y". Observe that, if n = 0 or 1, the Bemoulli equation is linear. For other values of n the substitution -y transforms the Bernoulli equation into the linear equation + (1 - n)P(x)u = (1 - 1)(a). Use an appropriate substitution to solve the equation and find the solution that satisfies y(1) = 1. Preview...
Solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form...
Solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form y' + P(x)y = Q(x)yn that can be reduced to a linear form by a substitution. The general solution of a Bernoulli equation is y1 − ne∫(1 − n)P(x) dx = (1 − n)Q(x)e∫(1 − n)P(x) dxdx+C (Enter your solution in the form F(x, y) = C or y = F(x, C) where C is a needed constant.) y8y' − 2y9 = exs
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) An equation in the form y + p(x)y -(x)y with n 0, 1 is...
1 point) An equation in the form y + p(x)y -(x)y with n 0, 1 is called a Bernoulli equation and it can be solved using the substitution wich transforms the Bernoulli equation into the following first order linear equation for v: Given the Bernoulli equation we have n- We obtain the equation u' Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by Then transforming back into the variables...
Consider the differential equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients...
Consider the differential
equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p
and q are continuous on some open interval I. Choose some point t0
in I. Let y1 be the solution of equation (1) that also satisfies
the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the
solution of equation (1) that satisfies the initial conditions
y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set...
(1 point) A Bernoulli differential equation is one of the form dete+ P(x)y= Q(2)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 am + (1 – n)P(x)u = (1 – n)Q(x). Use an appropriate substitution to solve the equation and find the solution that satisfies y(1) = 1. y(x) =
(15 points) A Bernoulli differential equation is one of the form dy dar + 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 + (1 - n)P(x) = (1 - nQ(x). dx Use an appropriate substitution to solve the equation xy' +y=2xy? and find the solution that satisfies y(1) = 1.
(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) =...
Fill in the blanks
(1 point) A Bernoulli differential equation is one of the form dy + P()y= Q(Cy" (*) dr 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 dac + (1 - n)P(x)u= (1 - nQ(2). Consider the initial value problem xy' +y= -6xy?, y(1) = -2. (a) This differential equation can be written in the form...
HW 2.4: Problem 3 Previous Problem Problem List Next Problem (1 point) A Bernoulli differential equation is one of the form + P(x)y -- Q(x)y". Observe that, if n = 0 or 1, the Bemoulli equation is linear. For other values of n the substitution -y transforms the Bernoulli equation into the linear equation + (1 - n)P(x)u = (1 - 1)(a). Use an appropriate substitution to solve the equation and find the solution that satisfies y(1) = 1. Preview...
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) An equation in the form y + p(x)y -(x)y with n 0, 1 is called a Bernoulli equation and it can be solved using the substitution wich transforms the Bernoulli equation into the following first order linear equation for v: Given the Bernoulli equation we have n- We obtain the equation u' Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by Then transforming back into the variables...
Consider the differential
equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p
and q are continuous on some open interval I. Choose some point t0
in I. Let y1 be the solution of equation (1) that also satisfies
the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the
solution of equation (1) that satisfies the initial conditions
y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set...
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