a) Solve the given differential equation by separation of variables. đ đđ 2 đ„đđŠ + đđ đ đŠđđ„ = 0

Zeeshan Ismail
2022-10-02

a) Solve the given differential equation by separation of variables. đ đđ 2 đ„đđŠ + đđ đ đŠđđ„ = 0

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asked 2022-11-01

Find the general solution to the differential eq: $({x}^{2}+{y}^{2})+xy{y}^{\xe2\x80\u010c}=0$

asked 2022-10-25

${u}_{xx}+{y}^{2}u=\mathrm{sin}\xe2\x81\u01042x$

I want to solve the non homogeneous differential equation

$$\frac{{\mathrm{\xe2\x88\x82}}^{2}u}{\mathrm{\xe2\x88\x82}{x}^{2}}+{y}^{2}u=\mathrm{sin}\xe2\x81\u01042x.$$

I have tried to solve it by method of separable of variables. But unfortunately, not able to find out the solution. Please give me some hints to solve it.

I want to solve the non homogeneous differential equation

$$\frac{{\mathrm{\xe2\x88\x82}}^{2}u}{\mathrm{\xe2\x88\x82}{x}^{2}}+{y}^{2}u=\mathrm{sin}\xe2\x81\u01042x.$$

I have tried to solve it by method of separable of variables. But unfortunately, not able to find out the solution. Please give me some hints to solve it.

asked 2022-10-30

Is the differential equation ${y}^{\xe2\x80\u010c}=x+y$ separable?

I'm at a loss. My guess is no, but I'm new to doing these problems. It can not be solved with cross multiplication but there are other ways of solving these problems I'm sure. Thank you for any help.

I'm at a loss. My guess is no, but I'm new to doing these problems. It can not be solved with cross multiplication but there are other ways of solving these problems I'm sure. Thank you for any help.

asked 2022-09-15

Show substitution leads to a separable differential equation.

Consider the differential equation...

${y}^{\xe2\x80\u010c}=f(\frac{y}{t})$

Show that the substitution $v=\frac{v}{t}$ leads to a separable differential equation in v

Here's what I did.

$v=\frac{y}{t}$

$\frac{dv}{dt}=\frac{dy}{dt}\xe2\x88\x92\frac{1}{{t}^{2}}$

Sub into the orignal.

$\frac{dv}{dt}=f(v)\xe2\x88\x92\frac{1}{{t}^{2}}$

$\frac{dv}{f(v)}=\frac{1}{{t}^{2}}dt$

This is where I get stuck. Is this the what the question is asking for, or am I forgetting to do something?

Consider the differential equation...

${y}^{\xe2\x80\u010c}=f(\frac{y}{t})$

Show that the substitution $v=\frac{v}{t}$ leads to a separable differential equation in v

Here's what I did.

$v=\frac{y}{t}$

$\frac{dv}{dt}=\frac{dy}{dt}\xe2\x88\x92\frac{1}{{t}^{2}}$

Sub into the orignal.

$\frac{dv}{dt}=f(v)\xe2\x88\x92\frac{1}{{t}^{2}}$

$\frac{dv}{f(v)}=\frac{1}{{t}^{2}}dt$

This is where I get stuck. Is this the what the question is asking for, or am I forgetting to do something?

asked 2022-11-10

Solve $x\frac{dy}{dx}\xe2\x88\x92y=({x}^{2}+{y}^{2})$

Solve the following differential equation -

$x\frac{dy}{dx}\xe2\x88\x92y=({x}^{2}+{y}^{2}).$

It most probably involves a change of variables so that it becomes variable separable.

Solve the following differential equation -

$x\frac{dy}{dx}\xe2\x88\x92y=({x}^{2}+{y}^{2}).$

It most probably involves a change of variables so that it becomes variable separable.

asked 2022-11-03

How can i solve this separable differential equation with trigonometric function?

The given Problem is separable differential equation:

$\mathrm{cos}\xe2\x81\u0104y\text{\xc2}dx+(1+{e}^{\xe2\x88\x92x})\mathrm{sin}\xe2\x81\u0104y\text{\xc2}dy=0$

$y(0)=\frac{\mathrm{\xcf\x80}}{4}$

The given Problem is separable differential equation:

$\mathrm{cos}\xe2\x81\u0104y\text{\xc2}dx+(1+{e}^{\xe2\x88\x92x})\mathrm{sin}\xe2\x81\u0104y\text{\xc2}dy=0$

$y(0)=\frac{\mathrm{\xcf\x80}}{4}$

asked 2022-09-30

Solving a separable differential equation: What's wrong with my calculation?

Solve the following separable differential equation:

$\frac{dy}{dx}=(\xe2\x88\x924)\xe2\x8b\x85{e}^{y}\xe2\x8b\x85cos(4x)$

Solve the following separable differential equation:

$\frac{dy}{dx}=(\xe2\x88\x924)\xe2\x8b\x85{e}^{y}\xe2\x8b\x85cos(4x)$