Solve the equation:

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

Line
2021-03-22
Answered

Solve the equation:

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

You can still ask an expert for help

Malena

Answered 2021-03-24
Author has **83** answers

The answer is in the video

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Let ${y}_{1}$ and ${y}_{2}$ be solution of a second order homogeneous linear differential equation ${y}^{\u2033}+p(x){y}^{\prime}+q(x)=0$ , in R. Suppose that ${y}_{1}(x)+{y}_{2}(x)={e}^{-x}$ ,

$W[{y}_{1}(x),{y}_{2}(x)]={e}^{x}$ , where $W[{y}_{1},{y}_{2}]$ is the Wro

ian of${y}_{1}$ and ${y}_{2}$ .

Find p(x), q(x) and the general form of${y}_{1}$ and ${y}_{2}$ .

ian of

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Consider, $ay{}^{\u2033}+b{y}^{\prime}+cy=0$ and $a\ne 0$ Which of the following statements are always true?

1. A unique solution exists satisfying the initial conditions$y\left(0\right)=\pi ,\text{}{y}^{\prime}\left(0\right)=\sqrt{\pi}$

2. Every solution is differentiable on the interval$(-\mathrm{\infty},\mathrm{\infty})$

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.

1. A unique solution exists satisfying the initial conditions

2. Every solution is differentiable on the interval

3. If

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