eliaskidszs
2021-12-28
Answered

Find general solutions (implicit if necessary, explicit if convenient) of the differential equations in Problem. Primes denote derivatives with respect to x.

$\frac{dy}{dx}={\left(64xy\right)}^{\frac{1}{3}}$

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deginasiba

Answered 2021-12-29
Author has **31** answers

Here, C is the constant of integration,

Suppose

Rewrite the solution as

temnimam2

Answered 2021-12-30
Author has **36** answers

karton

Answered 2022-01-09
Author has **439** answers

or,

Integrating, we get,

or,

or,

or,

which is the required general solution, where c be an arbitrary constant.

or,

Integrating,

or,

or,

Required general solution:

asked 2022-05-21

is there a method to solve

$\frac{dy}{dx}}=f(x,y)$

where $f(x,y)$ is a homogeneous function. I found some examples like $f(x,y)=(x+y{)}^{2}$ where it can be solved after converting it to Ricatti's equation.

thanks

$\frac{dy}{dx}}=f(x,y)$

where $f(x,y)$ is a homogeneous function. I found some examples like $f(x,y)=(x+y{)}^{2}$ where it can be solved after converting it to Ricatti's equation.

thanks

asked 2022-06-08

1. Can someone help me solve the following system of differential equations?

$\begin{array}{rcl}\frac{d{P}_{0}}{dt}& =& -{C}_{1}\lambda {P}_{0}{P}_{1}+\frac{{C}_{1}}{2}{P}_{1}^{2}\\ \frac{d{P}_{1}}{dt}& =& -{C}_{2}{P}_{1}+{C}_{1}\lambda {P}_{0}{P}_{1}-\frac{1}{2}(1+\lambda ){C}_{1}{P}_{1}^{2}+{C}_{1}{P}_{1}{P}_{2}\\ \frac{d{P}_{2}}{dt}& =& {C}_{2}{P}_{1}+\frac{{C}_{1}}{2}\lambda {P}_{1}^{2}-{C}_{1}{P}_{1}{P}_{2}\end{array}$

2. (Extending above) Suppose we have $K$ first order non-linear differential equations (similar to above), is there any simple method to solve them analytically?

$\begin{array}{rcl}\frac{d{P}_{0}}{dt}& =& -{C}_{1}\lambda {P}_{0}{P}_{1}+\frac{{C}_{1}}{2}{P}_{1}^{2}\\ \frac{d{P}_{1}}{dt}& =& -{C}_{2}{P}_{1}+{C}_{1}\lambda {P}_{0}{P}_{1}-\frac{1}{2}(1+\lambda ){C}_{1}{P}_{1}^{2}+{C}_{1}{P}_{1}{P}_{2}\\ \frac{d{P}_{2}}{dt}& =& {C}_{2}{P}_{1}+\frac{{C}_{1}}{2}\lambda {P}_{1}^{2}-{C}_{1}{P}_{1}{P}_{2}\end{array}$

2. (Extending above) Suppose we have $K$ first order non-linear differential equations (similar to above), is there any simple method to solve them analytically?

asked 2021-09-07

Take the Inverse Laplace Transform of the function.

$F\left(s\right)=\frac{1}{s({s}^{2}+2s+2)}$

asked 2021-12-29

Solve for the differential equations and get the general solution. Simplify your answer free from In. $dy=\mathrm{tan}x\mathrm{tan}ydx$

asked 2021-12-31

asked 2022-05-27

If I have a differential equation ${y}^{\prime}(t)=Ay(t)$ where A is a constant square matrix that is not diagonalizable(although it is surely possible to calculate the eigenvalues) and no initial condition is given. And now I am interested in the fundamental matrix. Is there a general method to determine this matrix? I do not want to use the exponential function and the Jordan normal form, as this is quite exhausting. Maybe there is also an ansatz possible as it is for the special case, where this differential equation is equivalent to an n-th order ode. I saw a method where they calculated the eigenvalues of the matrix and depending on the multiplicity n of this eigenvalue they used an exponential term(with the eigenvalue) and in each component an n-th order polynomial as a possible ansatz. Though they only did this, when they were interested in a initial value problem, so with an initial condition and not for a general solution.

I was asked to deliver an example: so ${y}^{\prime}(t)=\left(\begin{array}{cc}3& -4\\ 1& -1\end{array}\right)y(t)$ If somebody can construct a fundamental matrix for this system, than this should be sufficient

I was asked to deliver an example: so ${y}^{\prime}(t)=\left(\begin{array}{cc}3& -4\\ 1& -1\end{array}\right)y(t)$ If somebody can construct a fundamental matrix for this system, than this should be sufficient

asked 2020-12-28

To find:

The Laplace transform of$L[{e}^{-3t}{t}^{4}]$

The Laplace transform of