Answer to Question #131314 in Differential Equations for Pramod Pammu

Question

(y 2 +yz)dx+(xz+z 2 )dy+(y 2 −xy)dz=0 here P= (y^2+yz) , Q=(xz+z^2) , R=(y^2-xy)

Answer 1

As per the question,

given differential equation is

($y^2+yz)dx+(xz+z^2)dy+(y^2-xy)dz=0$ .....(equation 1)

Where

$y^2+yz=P$ ,

$xz+z^2=Q$ ,

$y^2-xy=R$

Integrate equation 1 ,

$(y^2+yz)x+c_1+(xz+z^2)y+c_2+(y^2-xy)z+c_3=0$

Where c$_1,c_2,c_3$ are constant of integration

$Px+Qy+Rz+C=0$

where C=$c_1+c_2+c_3$

Hence the solution of given differential is

Px+Qy+Rz+C=0