Question

Using homogenous equation , solve , ( x^2 + y^2 ) dx + xydy = 0

Answer 1

divide both sides by x^2 and see if it helps your case.

Answer 2

Skylar needs $56 to buy a new video game. If he doubles the amount of money he has now, he will have enough to buy the game with $8 left over.

How much money does Skylar have right now

Answer 3

sagutin ko hahaha

Answer 4

aha bat nandito ka

Answer 5

nandun na ko sa may ln|x| + 1/2| 1 + 2v^2 |

Answer 6

Guys, i arrived at ln|x| + 1/2 | 1+2v^2 | = 0 , i can't simplify it

Answer 7

let y=vx
dy=vdx + xdv

substitute:
\[(x^{2}+v^2x^2)dx+vx^2(vdx+xdv)=0\]

\[x^2dx+v^2x^2dx+v^2x^2dx+v^3dv=0\]

\[x^2dx+2v^2x^2dx+vx^3dv=0\]

\[x^2(1+2v^2)dx+vx^3dv=0 ] \frac{ 1 }{ x^3(1+2v^2) }\]

\[\int\limits_{}^{}\frac{ dx }{ x }+\int\limits_{}^{}\frac{ vdv }{ 1+2v^2 }=0\]

\[4(lnx+\frac{ 1 }{ 4 }\ln \left| 1+2v^2 \right|=c\]

\[4lnx+\ln \left| 1+2v^2 \right|=4c\]
\[lnx^{4}+\ln \left| 1+2v^2 \right|=4c\]
\[\ln \left\{ x^4\left( 1+2v^2 \right) \right\}=4c\]
let v=\[\frac{ y }{ x }\]

Answer 8

di pa tapos

Answer 9

substitute mo value ng v sa \[\ln{x^4(1+2v^2)}=4c\]

Answer 10

bukas nlng haha