Differential Equation

Calculus Level 3

$(3y-7x+7)dx+(7y-3x+3)dy=0$

Given: $y(1)= 0$

Then: $y(?)=2$

4 -3 -1 -2

1 solution

Sid Patak
Jul 13, 2017

Let $x=t+1$ $dx=dt$

Equation become homogenous so substitute: put $y=ut$ $dy=tdu+udt$

Now apply separation of variables and backtrack to get:

$(y+x-1)^5(y-x+1)^2=C$

Given y(1)=0 $(y+x-1)^5(y-x+1)^2=0$ or $y=1-x$ and $y=x-1$

$y(?)=2$ $?=-1,3$