solve the IVP

Thanks in advance.

Rivka Thorpe
2020-12-27
Answered

solve the IVP

Thanks in advance.

You can still ask an expert for help

liingliing8

Answered 2020-12-28
Author has **95** answers

The characteristic equation is

The roots of characteristic equation are :

Then the general solution of homogeneous equation is :.........(i)

Then

Using initial values in (i) and (ii), find c1 and c2 and then write the general solution.

asked 2022-06-25

Need help with this differential equation:

$\sqrt{3+{y}^{2}}dx-xdy={x}^{2}dy$

I began with variable separable method. So, already had done this:

$\sqrt{3+{y}^{2}}dx=({x}^{2}+x)dy$

$\frac{dx}{{x}^{2}+x}=\frac{dy}{\sqrt{3+{y}^{2}}}$

$\int \frac{dx}{{x}^{2}+x}=\int \frac{dy}{\sqrt{3+{y}^{2}}}$

Now I should solve that two integrals, but have some trouble with them and need your help. Also, I need help, explanation how to draw phase portrait for this equation, maybe some useful material about that?

$\sqrt{3+{y}^{2}}dx-xdy={x}^{2}dy$

I began with variable separable method. So, already had done this:

$\sqrt{3+{y}^{2}}dx=({x}^{2}+x)dy$

$\frac{dx}{{x}^{2}+x}=\frac{dy}{\sqrt{3+{y}^{2}}}$

$\int \frac{dx}{{x}^{2}+x}=\int \frac{dy}{\sqrt{3+{y}^{2}}}$

Now I should solve that two integrals, but have some trouble with them and need your help. Also, I need help, explanation how to draw phase portrait for this equation, maybe some useful material about that?

asked 2021-09-07

Use Laplace transform to solve the initial-value problem

asked 2022-06-27

I was solving differential equation

$x\mathrm{cos}x\frac{dy}{dx}+y(x\mathrm{sin}x+\mathrm{cos}x)=1$

which on dividing by $x\mathrm{cos}x$ becomes FOLD(first order linear differential) equation.

But I am stuck at following integral. Can anyone help solve this integral? An alternate approach to the problem is also welcome.

$\int \frac{{e}^{\mathrm{cos}x}}{\mathrm{cos}x}dx$

$x\mathrm{cos}x\frac{dy}{dx}+y(x\mathrm{sin}x+\mathrm{cos}x)=1$

which on dividing by $x\mathrm{cos}x$ becomes FOLD(first order linear differential) equation.

But I am stuck at following integral. Can anyone help solve this integral? An alternate approach to the problem is also welcome.

$\int \frac{{e}^{\mathrm{cos}x}}{\mathrm{cos}x}dx$

asked 2021-02-08

Q. 2# $(x+1)\frac{dy}{dx}=x({y}^{2}+1)$

asked 2022-04-15

Find the Laplace transform of $f\left(t\right)=10t{e}^{-5t}$

asked 2020-10-31

Use the Laplace transform to solve the given initial-value problem

$y{}^{\u2033}+2{y}^{\prime}+y=0,y\left(0\right)=1,{y}^{\prime}\left(0\right)=1$

asked 2021-03-05

Solve differential equation
$dy/dx-12{x}^{3}y={x}^{3}$