Detailed Explanations for Calculus 2 Equations

What is a solution to the differential equation $\frac{d y}{d x} = \frac{1 + x}{x y}$ with y(1)=-4?

Papierskiix5n 2022-04-16

What is a solution to the differential equation $\frac{d y}{d x} = (1 + x) (1 + y)$ ?

Mina Whitehead 2022-04-16

What is a solution to the differential equation $(x^{2}) (e^{y}) \frac{d y}{d x} = 4$ ?

Emmy Decker 2022-04-16

What is a solution to the differential equation $(1 + y) \frac{d y}{d x} - 4 x = 0$ ?

Reagan Gomez 2022-04-16

What is a solution to the differential equation $(\frac{d y}{d x}) - y - e^{3 x} = 0$ ?

Ekwadorkadba3 2022-04-16

What is a particular solution to the differential equation $\frac{d y}{d x} = 2 x y$ with y(0)=3?

alahovom7ahc 2022-04-16

What is a general solution to the differential equation $1 + y^{2} = y^{'} \sqrt{1 - x^{2}} = 0$ ?

zdebe5l8 2022-04-16

What is a particular solution to the differential equation $\frac{d y}{d x} = - \frac{x}{y}$ with y(4)=3?

Ean Hughes 2022-04-16

How do we go from
$\frac{1}{1 + (\frac{x}{2}) + (\frac{x^{2}}{3}) + (\frac{x^{3}}{4}) + \dots}$

fernandoval3sbr 2022-04-15

Method of Undetermined Coefficients using X's on left hand side
I have a couple questions on this question.
The question is asking me to find the general solution to
$x^{″} + 6 x^{'} + 9 x = \cos (2 t) + \sin (2 t) .$
Solving for the general solution, I got
$Y_{c} = C_{1} e^{- 3 x} + C_{2} x e^{- 3 x}$ .
I was wondering if the fact that the left hand side uses x's instead of y's matters? For almost every question, it uses y's instead of x's.
Also, for $Y_{p}$ . I got $Y_{p} = A \cos (2 t) + B \sin (2 t)$ .
I ultimately got the answer to be
$C_{1} e^{- 3 x} + C_{2} x e^{- 3 x} - (7 \frac{\cos (2 t)}{169}) + (17 \frac{\cos (2 t)}{169}),$
which I do not feel to be correct.

Willie Kelley 2022-04-15

Laplace Transform piecewise function with domain from 1 to inf
$f (t) = {\begin{cases} t - 1 1 \leq t < 2 \\ 3 - t 2 \leq t < 3 \\ 0 t \geq 3 \end{cases}$

Cash Duncan 2022-04-15

Is this initial-value problem separable?
I have $\frac{d y}{d x} = \frac{2 (x^{3} + x^{2} - x + 1) y}{x^{4} - 1},; y (0) = 1 .$
I tried separating it and got $2 y^{- 1} d y = (x^{3} + x^{2} - x + 1) {(x^{4} - 1)}^{- 1}$
I am unsure if that separation is correct, would anyone be able to clarify?

Yaritza Estrada 2022-04-15

Is there a way to solve this O.D.E without using Lagrange equation method?
$x {(y^{'})}^{2} - y y^{'} = - 1$

Breanna Fisher 2022-04-15

Find orthogonal trajectories of the function $y = c x^{2}$

Adison Palmer 2022-04-15

How do I solve this second-order differential equation?
I want to find $θ (t)$ and I have the following differential equation:
$\frac{d^{2} θ}{{d t}^{2}} = 5.36 \sin θ - 0.028 {(\frac{d θ}{d t})}^{2}$
${(\frac{d θ}{d t})}^{2}$ is the square of the first derivative of $θ (t)$ .

wijive3510 2022-04-14

Construct a 95% confidence interval for the true average monthly salary earned by all employees of People Plus Pty, if it was found that the average monthly salary earned by a sample of 19 employees of the company was R18 500, with a standard deviation of R1 750. Interpret your answer

Alivia Rojas 2022-04-14

Is there any way to solve it?
$min {2, \frac{n}{2}} + min {3, \frac{n}{2}} + min {4, \frac{n}{2}} + \dots + min {n + 1, \frac{n}{2}} = \sum_{i = 1}^{n} min (i + 1, \frac{n}{2})$

Elijah Schwartz 2022-04-14

Is there an intuition behind the Euler Lagrange equation?
I am taking calculus of variations at the moment and I am curious if there is a visualization of why the EL must be satisfied for all extremals.
At first glance it's hard for me to relate:
$\frac{d}{d x} (\frac{\partial L}{\partial y^{'}}) = \frac{\partial L}{\partial y}$
With a geometric/visual intuition.

Perla Benitez 2022-04-14

Find p(t) for the ODE given that the Wro
ian is a non-zero constant.
Consider an ODE of the form $\frac{d^{2} x}{{d t}^{2}} + p (t) \frac{d x}{d t} + q (t) x = 0$
Suppose that we have two solutions $x_{1} (t) and x_{2} (t)$ to this ODE and their Wro
ian is a non-zero constant. That is,
$W [x_{1}, x_{2}] = C \neq 0$
What is p(t)? (Find an explicit formula).
The formula for the Wro
ian is
$W [x_{1}, x_{2}] = x_{1} \frac{{d x}_{2}}{d t} - x_{2} \frac{{d x}_{1}}{d t}$
Since the Wro
ian is non-zero, we know that x1 and x2 are independent. This means that $\frac{{d x}_{1}}{d t}$ and $\frac{{d x}_{2}}{d t}$ are such that all variables cancel out. I'm not sure how to proceed from here. Can I get some hints on how to find p(t)? Thanks
Edit: Using Abel's theorem, we know that if $x_{1} and x_{2}$ are solutions to the ODE then
$W [x_{1}, x_{2}] = A e^{- \int p (t) d t}$
Then this can be used to solve for p(t).
$\begin{aligned} W [x_{1}, x_{2}] & = A e^{- \int p (t) d t} = C \\ e^{- \int p (t) d t} = \frac{C}{A} \\ \int p (t) d t = - \ln (\frac{C}{A}) \\ p (t) = \frac{d}{d t} (- \ln (\frac{C}{A})) \\ = 0 \end{aligned}$
So $p (t) = 0$ .

Mary Bates 2022-04-14

Difficulty in evaluating
$lim_{t \to x} \frac{t^{2} f (x) - x^{2} f (t)}{t - x}$

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.

Calculus 2

Calculus 2 Equations: Expert Solutions and More