find the general solution for the following homogeneous equations. show solutions
1) (xy+y2)dx−x2dy=0 (hint: let u=y/x, so y=ux, dy=xdu+udx))
2) 2x2ydx=(3x3+y3)dy. (hint: let v=x/y, so x=vy, dx=vdy+ydv)

Follow the hints.

1. Let , so that and . Substituting into

gives

and the remaining ODE is separable:

Integrate both sides to get

2. , so that and . Then

becomes

which is separable as

Integrating both sides gives

i can you with this sweetie!

step-by-step explanation:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.