manudyent7
2022-09-12
Answered

How do you determine the derivative of xcosx?

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asked 2022-09-12

How to you find the general solution of $(2+x)y\prime =3y$?

asked 2022-07-13

I have difficulties to solve these two differential equations:

1) ${y}^{\prime}(x)=\frac{x-y(x)}{x+y(x)}$ with the initial condition $y(1)=1$ .I'm arrived to prove that

$y=x(\sqrt{2-{e}^{-2(\mathrm{ln}x+c)}}-1)$

but I don't know if it's correct. If it's right, how do I find the constant $c$? Because WolframAlpha says that the solution is $y(x)=\sqrt{2}\sqrt{{x}^{2}+1}-x$.

2) ${y}^{\prime}(x)=\frac{2y(x)-x}{2x-y(x)}$. I'm arrived to prove that $\frac{z-1}{(z+1{)}^{3}}={e}^{2c}{x}^{2}$ but I don't know if it's correct. If it's right, how do I explain $z$ to substitute it in $y=xz$? Then, how do I find the constant $c$ ?

1) ${y}^{\prime}(x)=\frac{x-y(x)}{x+y(x)}$ with the initial condition $y(1)=1$ .I'm arrived to prove that

$y=x(\sqrt{2-{e}^{-2(\mathrm{ln}x+c)}}-1)$

but I don't know if it's correct. If it's right, how do I find the constant $c$? Because WolframAlpha says that the solution is $y(x)=\sqrt{2}\sqrt{{x}^{2}+1}-x$.

2) ${y}^{\prime}(x)=\frac{2y(x)-x}{2x-y(x)}$. I'm arrived to prove that $\frac{z-1}{(z+1{)}^{3}}={e}^{2c}{x}^{2}$ but I don't know if it's correct. If it's right, how do I explain $z$ to substitute it in $y=xz$? Then, how do I find the constant $c$ ?

asked 2022-09-08

What is a solution to the differential equation $y\prime -y=5$?

asked 2022-09-09

What is the particular solution of the differential equation? : $y\prime +4xy={e}^{-2{x}^{2}}$ with y(0)=−4.3

asked 2022-01-20

Solve the first order differential equation using any acceptable method.

$\mathrm{sin}\left(x\right)\frac{dy}{dx}+\left(\mathrm{cos}\left(x\right)\right)y=0$ , $y\left(\frac{7\pi}{6}\right)=-2$

asked 2022-01-20

Let y be a function of x. Which of the following is a first order linear differential equation?

$1.{y}^{\prime}-x={y}^{2}\mathrm{sin}\left(x\right)$

$2.{y}^{\prime}-x=y\mathrm{sin}\left(x\right)$

$3.{\left({y}^{\prime}\right)}^{2}+y=\mathrm{tan}\left(2x\right)$

$4.{y}^{\prime}={y}^{2}{e}^{x}$

$5.{\left({y}^{\prime}\right)}^{2}+y={e}^{x}$

asked 2022-01-21

Write an equivalent first-order differential equation and initial condition for y.

What is the equivalent first-order differential equation?

What is the initial condition?