Question

given that y(2-x)=3, show that 3 d2y/dx2 - 2y dy/dx = 0

Answer 1

@ganeshie8 Not able to find? :(

Answer 2

y(2-x) = 3

differentiate both sides with respect to x and get

y'(2-x) + y(-1) = 0

Answer 3

replace 2-x by 3/y :
y'*3/y - y = 0

multiply y through out
3y' - y^2 = 0

Answer 4

differentiate through out again and you're done!

Answer 5

THANKS!!!! I have another question!

Given that y=(1+4x)e^-2x , show that d2y/dx2 + 4 dy/dx + 4y = 0

Answer 6

@ganeshie8

Answer 7

y = (1+4x)e^-2
y' = ?

Answer 8

U have to follow the same method of differentiation in this problem as was described by @ganeshie8

Answer 9

\[y e{2x}=1+4x\]
diff. twice w.r.t. x
\[y~e ^{2x}2+e ^{2x}\frac{ dy }{ dx }=4\]
\[2~y~e ^{2x}2+2~e ^{2x}\frac{ dy }{ dx }+e ^{2x}\frac{ d^2y }{ dx^2 }+2~e ^{2x}\frac{ dy }{ dx }=0\]
divide by
\[e{2x}\]
\[4y+4\frac{ dy }{ dx }+\frac{ d^2y }{ dx^2 }=0\]