Question

Solve the differential equation
(y² + z²-x²) dx - 2xydy - 2xz dz =0 ​

Answer 1

Step-by-step explanation:

now dy/2xy=dz/2xz

can cel 2x we get dy/y=dz/z

Integrate we get logy= logz or y=c1z , c1 is constant ……….(1)

Now Consider: dx/(y^2 + z^2 -x^2) = dz/2xz …………(2)

Putting y=cz in (2) above we get

dx/(c1^2z^2 +z^2 +x^2) = dz/z

Now solvehis equation

suppose its solution is Function of (x,z)=c2 and (1) above together constitute the solution

the solution is f(y/z,c2)=0

where c2 is replaced by function of (x,z))=0 is the soln.