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Attempt 1: 3 out of 9 parts have been answered correctly. A Bernoulli differential equation is one of the form $\frac{dy}{dx} + P(x)y = Q(x)y^n$ () Observe that, if $n = 0$ or 1, the Bernoulli equation is linear. For other values of $n$, the substitution $u = y^{1-n}$ transforms the Bernoulli equation into the linear equation $\frac{du}{dx} + (1 - n)P(x)u = (1 - n)Q(x)$. Consider the initial value problem $xy' + y = 9xy^2$, $y(1) = 9$. (a) This differential equation can be written in the form () with $P(x) = \frac{1}{x}$, $Q(x) = 9$, and $n = 2$ (b) The substitution $u =$ $\frac{du}{dx} +$ (c) Using the substitution in part (b), we rewrite the initial condition in terms of $x$ and $u$: $u(1) =$ (d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c). $u(x) =$ (e) Finally, solve for $y$. $y(x) =$ Try again Next item

          Attempt 1: 3 out of 9 parts have been answered correctly.
A Bernoulli differential equation is one of the form
$\frac{dy}{dx} + P(x)y = Q(x)y^n$ (*)
Observe that, if $n = 0$ or 1, the Bernoulli equation is linear. For other values of $n$, the substitution $u = y^{1-n}$ transforms the Bernoulli equation into the linear equation
$\frac{du}{dx} + (1 - n)P(x)u = (1 - n)Q(x)$.
Consider the initial value problem
$xy' + y = 9xy^2$, $y(1) = 9$.
(a) This differential equation can be written in the form (*) with
$P(x) = \frac{1}{x}$,
$Q(x) = 9$, and
$n = 2$
(b) The substitution $u =$
$\frac{du}{dx} +$
(c) Using the substitution in part (b), we rewrite the initial condition in terms of $x$ and $u$:
$u(1) =$
(d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c).
$u(x) =$
(e) Finally, solve for $y$.
$y(x) =$
Try again Next item

Show more…

Attempt 1: 3 out of 9 parts have been answered correctly.
A Bernoulli differential equation is one of the form
(dy)/(dx) + P(x)y = Q(x)y^n (*)
Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y^1-n transforms the Bernoulli equation into the linear equation
(du)/(dx) + (1 - n)P(x)u = (1 - n)Q(x).
Consider the initial value problem
xy' + y = 9xy^2, y(1) = 9.
(a) This differential equation can be written in the form (*) with
P(x) = (1)/(x),
Q(x) = 9, and
n = 2
(b) The substitution u =
(du)/(dx) +
(c) Using the substitution in part (b), we rewrite the initial condition in terms of x and u:
u(1) =
(d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c).
u(x) =
(e) Finally, solve for y.
y(x) =
Try again Next item

Added by Daniel D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vikash Ranjan

05/28/2022

Step 1

Step 1: Identify the given Bernoulli differential equation in the form (dy)/(dx) + P(x)y = Q(x)y^n Given equation: xy' + y = 9xy^2 Show more…

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Attempt 1: 3 out of 9 parts have been answered correctly. A Bernoulli differential equation is one of the form (dy)/(dx)+P(x)y=Q(x)y^(n) Observe that, if n=0 or 1 , the Bernoulli equation is linear. For other values of n, the substitution u=y^(1-n) transforms the Bernoulli equation into the linear equation (du)/(dx)+(1-n)P(x)u=(1-n)Q(x). Consider the initial value problem xy^(')+y=9xy^(2),y(1)=9. (a) This differential equation can be written in the form (**) with P(x)=◻ Q(x)=◻^(◻) n= (b) The substitution u= (du)/(dx)+| u= (c) Using the substitution in part (b), we rewrite the initial condition in terms of x and u : u(1)= (d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c). u(x)= (e) Finally, solve for y. y(x)= Attempt 1: 3 out of 9 parts have been answered correctly A Bernoulli differential equation is one of the form dx 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 dr Consider the initial value problen xy+y=9xyy1=9 a) This differential equation can be written in the form (*) with P= x Qx)= and n= (b The substitution u du xp will transform it into the linear equation (c) Using the substitution in part (b), we rewrite the initial condition in terms of x and u: 1= (d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c) u(x)= e Finally,solve for y yx= Try again Next item

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