Solve differential equation

Jaden Easton
2020-12-28
Answered

Solve differential equation

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asked 2022-09-08

What is a solution to the differential equation $\frac{dy}{dx}={e}^{x+y}$?

asked 2022-09-11

Solve $\frac{dy}{dx}-\frac{1}{2}(1+\frac{1}{x})y+\frac{3}{x}{y}^{3}=0$?

asked 2022-09-29

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

asked 2022-06-15

I have to find the form of the function $h(t)$ in this equation:

${h}^{\prime}(t)-\frac{\theta h(t)}{2}+1=0$

with $h(T)=C$ where $T$ and $C$ are constants and $T\ge 0$

At first I thought it was a Bernoulli differential equation and I tried:

$V(t)=\frac{1}{h(t)}\Rightarrow {V}^{\prime}(t)=\frac{{h}^{\prime}(t)}{h(t{)}^{2}}$

My equation becomes worse:

${V}^{\prime}(t)-\frac{\theta}{2}+\frac{1}{V(t{)}^{2}}=0$

Then I tried with the integrating factor:

$({e}^{t}h(t){)}^{\prime}=2{e}^{t}h(t)-{e}^{t}$

${e}^{t}h(t)=\int 2{e}^{t}h(t)-{e}^{t}$

I'm stuck here because $h(t)$ is not a variable, is a function and I have to find how it looks like.

Edit: I forgot: $\theta $ is a constant.

How can I solve this problem?

${h}^{\prime}(t)-\frac{\theta h(t)}{2}+1=0$

with $h(T)=C$ where $T$ and $C$ are constants and $T\ge 0$

At first I thought it was a Bernoulli differential equation and I tried:

$V(t)=\frac{1}{h(t)}\Rightarrow {V}^{\prime}(t)=\frac{{h}^{\prime}(t)}{h(t{)}^{2}}$

My equation becomes worse:

${V}^{\prime}(t)-\frac{\theta}{2}+\frac{1}{V(t{)}^{2}}=0$

Then I tried with the integrating factor:

$({e}^{t}h(t){)}^{\prime}=2{e}^{t}h(t)-{e}^{t}$

${e}^{t}h(t)=\int 2{e}^{t}h(t)-{e}^{t}$

I'm stuck here because $h(t)$ is not a variable, is a function and I have to find how it looks like.

Edit: I forgot: $\theta $ is a constant.

How can I solve this problem?

asked 2022-09-30

What is the solution of the differential equation? : $y\frac{dy}{dx}={(9-4{y}^{2})}^{\frac{1}{2}}$ where x=0 when y=0

asked 2022-06-21

I have a differential equation of the form

$dy/dx+p(x)y=q(x)$

under the condition that $q(x)=300$ if $y<3312$ and $q(x)=0$ if $y\ge 3312$.

I could not understand how to solve this differential equation with such heavy side function ?

Any hints?

$dy/dx+p(x)y=q(x)$

under the condition that $q(x)=300$ if $y<3312$ and $q(x)=0$ if $y\ge 3312$.

I could not understand how to solve this differential equation with such heavy side function ?

Any hints?

asked 2021-05-31

Identify the surface whose equation is given.

$\rho =\mathrm{sin}\theta \mathrm{sin}\varphi $