# Expert Assistance for Separable Differential Equations: Comprehensive Resources and Practice Problems

Recent questions in Separable Differential Equations
nepojamanuszc 2023-03-23

## 1 degree on celsius scale is equal to A) $\frac{9}{5}$ degree on fahrenheit scaleB) $\frac{5}{9}$ degree on fahrenheit scaleC) 1 degree on fahrenheit scaleD) 5 degree on fahrenheit scale

goorst9Bi 2022-11-23

## Correct approach to this homogeneous differential equationI am trying to find the general solution to the following equation, but the integral at the end is very complicated and leads me to believe I may have made a mistake somewhere.$x{y}^{2}\frac{dy}{dx}={y}^{3}+x{y}^{2}-{x}^{2}y-{x}^{3}$Which, by the substitution $z=\frac{y}{x}$, can be rearranged into the equation$x\frac{dz}{dx}=1-\frac{1}{z}-\frac{1}{{z}^{2}}$This is a separable equation, which I separated into$\int \frac{1}{1-\frac{1}{z}-\frac{1}{{z}^{2}}}dz=\int \frac{1}{x}dx$The right-hand side is easy to solve, but the left-hand integral is giving me trouble. Assuming I did the steps leading up to it correctly, the integral has me stumped. Even WolframaAlpha is unhelpful. My first thought would be to try a partial fraction, but after a few attempts it does not seem to work.Am I approaching this differential equation correctly? Is there an error I haven't caught?

siotaody 2022-11-23

## Separation of variables differential equationSolve this equation by separation of variables: xu'=3u.I see that the answer should be u(x)=$c{x}^{3}$, but since I have no knowledge of differential equations, can someone provide the steps?

Juan Lowe 2022-11-23

## How to solve such fraction differential equation?Here's my first-order differential equation:$\left({x}^{3}-2x{y}^{2}\right)dx+3y{x}^{2}dy=xdy-ydx$I've tried to make it fraction, but it isn't separable differential equation, also it isn't differential equation in total differentials, so after it I lose any clue for answer.

quakbIi 2022-11-22

## How can i solve this separable differential equation?Given Problem is to solve this separable differential equation:${y}^{\mathrm{\prime }}=\frac{y}{4x-{x}^{2}}.$My approach: was to build the integral of y':$\int {y}^{\mathrm{\prime }}=\int \frac{y}{4x-{x}^{2}}dy=\frac{{y}^{2}}{2\left(4x-{x}^{2}\right)}.$But now i am stuck in differential equations, what whould be the next step? And what would the solution looks like? Or is this already the solution? I doubt that.P.S. edits were only made to improve language and latex

Kayley Dickson 2022-11-21

## Separable Differential EquationHow would you solve the next ODE?$\frac{dy}{dt}=\frac{at+by+m}{ct+dy+n},$where $a,b,c,d,m,n$ are constants and $ad=bc$Corrected.

Nicholas Hunter 2022-11-21

## Is $\left(2x+y\right)dx-xdy=0$ a separable differential equation?I was given the following differential equation in an assignment the other day:$\left(2x+y\right)dx-xdy=0$The problem specified to solve the equation using the method of separation of variables. My problem was setting the integral, I tried multiple manipulations with but nothing seemed to work. So, I have to ask can this equation be solved using separation of variables?

szklanovqq 2022-11-19

## Completing partial derivatives to make them convergeFor a function $f\left(x,y\right)$ of two independent variables we have an incomplete specification of its partial derivatives as follows:$\frac{\mathrm{\partial }f\left(x,y\right)}{\mathrm{\partial }x}=\frac{1}{g\left(x,y\right)\sqrt{1-\left(\frac{ky}{{x}^{\left(1/3\right)}}{\right)}^{2}}}$$\frac{\mathrm{\partial }f\left(x,y\right)}{\mathrm{\partial }y}=\left(\frac{3x}{4}\right){\left(\frac{k}{{x}^{\left(1/3\right)}}\right)}^{2}\left(2y\right)\frac{1}{g\left(x,y\right)\sqrt{1-\left(\frac{ky}{{x}^{\left(1/3\right)}}{\right)}^{2}}}$Problem: finding a suitable $g\left(x,y\right)$ that makes the partial derivatives converge to a single function $f\left(x,y\right)$ that fulfills the condition $f\left(x,0\right)=x$I will be grateful if people with many flight hours can offer suggestions for $g\left(x,y\right)$. Needless to say, I am not asking that they verify those suggestions, but in case someone would like, these are the inputs to Wolfram integrator:

Tiffany Page 2022-11-19

## How to solve $x{y}^{\prime }=2\sqrt{{x}^{2}+{y}^{2}}+y$?And what would be the standard form to illustrate this situation? (e.g. ${y}^{\prime }+P\left(x\right)y=Q\left(x\right)$ would be standard form of first order linear differential equation)

klasyvea 2022-11-19

## Separable Differential Equation dy/dt = 6yThe question is as follows:$\frac{dy}{dt}=6y$$y\left(9\right)=5$I tried rearranging the equation to $\frac{dy}{6y}=dt$ and integrating both sides to get $\left(1/6\right)\mathrm{ln}|y|+C=t$. After that I tried plugging in the 9 for y and 5 for t and solving but I can't quite seem to get it.

InjegoIrrenia1mk 2022-11-18

## Is there a solution for y for $\frac{dy}{dx}=ax{e}^{by}$I have come up with the equation in the form$\frac{dy}{dx}=ax{e}^{by}$, where a and b are arbitrary real numbers, for a project I am working on. I want to be able to find its integral and differentiation if possible. Does anyone know of a possible solution for $y$ and/or $\frac{{d}^{2}y}{d{x}^{2}}$?

Hayley Mcclain 2022-11-18

## All alternative solution for an equationI'm looking for all alternative solutions of this${x}^{\prime }=x\left(x-1\right)\left(x+1\right)$But I absolutely don't know what I have to do! Thanks!

Hanna Webster 2022-11-18

## Separable Differential Equation explainedSo i have the equation $\frac{dy}{dt}=1+y$looking at the answers my lecture has given it states$\frac{d}{dt}\left(1+y\right)=1+y$then $1+y\left(t\right)=A{e}^{t}$ where A is a constantCan someone explain these steps please?

klesstilne1 2022-11-17

## How do I find the singular solution of the differential equation ${y}^{\prime }=\frac{{y}^{2}+1}{xy+y}$?I start out with the separable differential equation,${y}^{\prime }=\frac{dy}{dx}=\frac{{y}^{2}+1}{xy+y}=\frac{{y}^{2}+1}{y\left(x+1\right)}$Thus, $\frac{1}{x+1}dx=\frac{y}{{y}^{2}+1}dy$Then integrating both sides of the equation, I get$\mathrm{ln}\left(x+1\right)=\frac{1}{2}\mathrm{ln}\left({y}^{2}+1\right)+C$Now, ${e}^{\mathrm{ln}\left(x+1\right)}$ = ${e}^{\frac{1}{2}\mathrm{ln}\left({y}^{2}+1\right)+C}$. So...$\left(x+1\right)={e}^{C}\left({y}^{2}+1{\right)}^{\frac{1}{2}}$I kind of wanted to know if this is indeed the correct general formula. And also, how would I find the singular solution, if there happens to be one in this case.

Arendrogfkl 2022-11-16

## Solving separable equations with dy/dx on both sides?I'm unsure on how to even start with this equation: $y-x\frac{dy}{dx}=1+{x}^{2}\frac{dy}{dx}$I thought it would be possible to cancel out but the answer was different. Could someone please provide a hint on how to start this equation? I thought about moving the $-x\frac{dy}{dx}$ over to the RHS and then group it under the common variable $\frac{dy}{dx}$ but the question was under the 'separable differential' section in my textbook so I don't think it's the correct method.

kunguwaat81 2022-11-15

## Separable differential equation ${x}^{2}{y}^{″}=2y$Show that ${x}^{2}-{x}^{-1}$ is a solution of${x}^{2}\frac{{\text{d}}^{2}y}{\text{d}{x}^{2}}=2y$I've tried separating the x and y terms and then integrating, but I could tell it wouldn't work. Any ideas? It's a simple question but I have not attempted them in a while.

Davirnoilc 2022-11-15

## a separable differential equationgiven this$\frac{d}{dx}=x\left(1-x\right)$where$x\left(0\right)=0.1$is this correct:?$\frac{dx}{dt}=x\left(1-x\right)$$t-{t}_{0}=\int \frac{dx}{x\left(1-x\right)}$Where did the t and ${t}_{0}$ come from?

Messiah Sutton 2022-11-15