Question

Please help solve y"-2(y')^2=0 using dy/dx=p

Answer 1

\[y"+2(y')^{2}=0 using \frac{ dy }{ dx }=\rho\]

Answer 2

let dy/dx = u

then you get du/dx + 2u^2 = 0 <-- this is first order DE use separation of variables
du/u^2 + 2dx = 0
-1/u + 2x + c_1 = 0
u = 1/(2x + c_1)

again we have u = dy/dx
dy/dx = 1/(2x+c_1)
dy = dx/(2x+c_1)
integrate both sides you will get
y = 1/2 log(2x+c_1) + c_2

Answer 3

The quest asks if u can use dy/dx=p

Answer 4

@ ajprincess

Answer 5

@moyo30 experimentX is right in solving this ques. He just used dy/dx = u instead of dy/dx = p .

Answer 6

thx

Answer 7

i c it now