Differential Equation Help: Solve with Confidence

College
Calculus and Analysis
Differential Equations

Recent questions in Differential Equations

Donald Johnson 2021-12-08

Please suggest a substitution for solving or any method of solving:
$y^{″} (x) \cot (y (x)) = y^{'} {(x)}^{2} + c$

evrimesa 2021-12-07

Take the Laplace transform of the following initial value and solve for Y(s)=L{y(t)}:

sin(π t), 0 ≤ t <1

y''+9y= { y(0)=0, y′(0)=0

0, 1 ≤ t

a) Y(s)= ? (Hint: write the right hand side in terms of the Heaviside function)

b) Now find the inverse transform to find y(t)= ? . (Use step(t-c) for uc(t) .)

Note= π/ (s^2+π^2)(s^2+9) = π/ π^2 -9 (1/(s^2+9) - 1/(s^2+ π^2)

interdicoxd 2021-12-07

Solve this differential equation:
$y^{″} - 7 y^{'} + 10 y = \cos x$
where y is a one-variable function x. What am I supposed to do with the cosx?

alka8q7 2021-11-23

I have the following differential equation:
$y + y = \cos (t) \cos (2 t)$
Maybe something can be done to $\cos (t) \cos (2 t)$ to make it easier to solve. Any ideas?

Schwelliney 2021-11-23

Solve the following differential equation: $1 + y' (x)^{2} - y'' (x) (y (x) - λ) = 0$

3kofbe 2021-11-23

Consider, $a y^{″} + b y^{'} + c y = 0$ and $a \neq 0$ Which of the following statements are always true?
1. A unique solution exists satisfying the initial conditions $y (0) = π, y^{'} (0) = \sqrt{π}$
2. Every solution is differentiable on the interval $(- \infty, \infty)$
3. If $y_{1}$ and $y_{2}$ are any two linearly independent solutions, then $y = C_{1} y_{1} + C_{2} y_{2}$ is a general solution of the equation.

danrussekme 2021-11-23

Solve th second order linear equations:
$y + 4 y = \cos 2 x$

Ronnie Baur 2021-11-23

Id

chanyingsauu7 2021-11-21

How can the following second-order linear equation be converted into a first-order linear equation?
This is our second-order equation:
$y^{″} - 2 y^{'} + 2 y = e^{2 t} \sin t$

Edmund Adams 2021-11-21

I need to find a second order linear homogeneous equation with constant coefficients that has the given function as a solution
Queston a) $x e^{- 3 x}$
Question b) $e^{3 x} \sin x$

khi1la2f1qv 2021-11-21

I am having trouble figuring out a method for finding a solution to
$r + (\frac{2}{r}) {(r^{'})}^{2} - r^{″} = 0$
I have tried substitution of $w = r^{'}$ to obtain
$r + (\frac{2}{r}) w^{2} = \frac{d w}{d r} w$
But then I am not sure how to proceed from there.
Any suggestions are welcome. Tha

Minerva Kline 2021-11-20

Is there any known method to solve such second order non-linear differential equation?
$y_{n} - n x \frac{1}{\sqrt{y_{n}}} = 0$

prelimaf1 2021-11-20

Find all first-order partial derivatives of the function at any point of the domain.
$f (x, y, z) = 4 x^{3} y^{2} - e^{z} y^{4} + \frac{z^{3}}{x^{2}} + 4 y - x^{16} + 2021$

Clifton Sanchez 2021-11-20

Find the general solution of the given higher-order differential equation. $y^{(4)} + y''' + y'' = 0, y (x) = ?$

Yolanda Jorge 2021-11-20

Show that $y = x^{2} \sin (x)$ and $y = 0$ are both solutions of
$x^{2} y^{″} - 4 x y^{'} + (x^{2} + 6) y = 0$
and that both satisfy the conditions $y (0) = 0$ and $y^{'} (0) = 0$ . Does this theorem contradict Theorem A? If not, why not?

Lloyd Allen 2021-11-20

Calculate. $\frac{d (2 x^{5})}{d x}$

protisvitfc 2021-11-19

I'm trying to find particular solution of the second-order linear equation but I can't find $y_{1}$ and $y_{2}$ according to $y = c_{1} y_{1} + c_{2} y_{2}$
$x^{2} y^{″} - 2 x y^{'} + 2 y = 0, y (1) = 3, y^{'} (1) = 1$
If r is used, $x^{2} r^{2} - 2 x r = - 2$ then $x r (x r - 2) = - 2$ , I can't go on from there to find $y_{1}$ and $y_{2}$

folklorahhe 2021-11-19

The differential equation is as follows: $(x + 1) y^{″} - (2 x + 3) y^{'} + (x + 2) y = 0$ where y(x) is a funtion on $R$ . First, I had to show that $y_{1} (x) = e^{x}$ is a solution for the DV. The second question was to find the general solution of the DV. I instantly started on the series of solution solving method, but I think I have to use the 'hint' $y_{1} (x) = e^{x}$ is a solution to the DV, but how to do this?

kiki195ms 2021-11-19

The identity
$\sum_{k = 0}^{\infty} a^{k} \cos (k x) = \frac{1 - a \cos x}{1 - 2 a \cos x + a^{2}}, | a | < 1$
can be derived by using the fact that $\sum_{k = 0}^{\infty} a^{k} \cos (k x) = R e \sum_{k = 0}^{\infty} {(a e^{i x})}^{k}$
But can it be derived without using complex variables?

Aufopferaq 2021-11-19

Differentiate.
$y = x \cos^{- 1} x$

Speaking of differential equations, these are used not only by those students majoring in Physics because solving differential equations is also quite common in Statistics and Financial Studies. Explore the list of questions and examples of equations to get a basic idea of how it is done.

These answers below are meant to provide you with the starting points as you work with your differential equations. If you need specific help or cannot understand the rules behind the answers that are presented below, start with a simple equation and learn with the provided solutions..

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