Question

2p²x + x = 2yp

please solve this

{ differential equation }

( Solvable for x y or z) ​

Answer 1

Step-by-step explanation:

2p²x+x=2yp

2p²2x=2yp

Answer 2

Answer:

2p²x + x = 2yp ; p² = ln(pc) - ln(x).

Step-by-step explanation:

Given  equation is

$2p^2x+x=2yp\;\;\;\;......i)\\\;\\(2p^2+1)x=2yp\\\;\\(2p^2+1)\frac{x}{2p}=y\\\;\\y=(p+\frac{1}{2p})x\\\;\\\text{Differentiating this equation with respect to x yields}\\\;\\\frac{dy}{dx}=x(\frac{dp}{dx}-\frac{1}{2p^2}.\frac{dp}{dx})+(p+\frac{1}{2p})\\\;\\p=x(1-\frac{1}{2p^2})\frac{dp}{dx}+(p+\frac{1}{2p})\\\;\\-\frac{1}{2p}=x(\frac{2p^2-1}{2p^2})\frac{dp}{dx}\\\;\\1=x(\frac{1-2p^2}{p})\frac{dp}{dx}\\\;\\\frac{dx}{x}=(\frac{1}{p}-2p)\frac{dp}{dx}\\\;\\\text{Integrating both sides}\\\;\\\ln x=\ln p-p^2+\ln c$

$p^2=\ln pc-\ln x\;\;\;\;\;\;\;.........ii)$

Since it is not possible to eliminate p between equation i) and ii).

Thus these two equations together will represent the required solution of given differential equation.

Hence Solution will be,

2p²x + x = 2yp ; p² = ln(pc) - ln(x).