First-Order Nonlinear Equations with Three or More Independent Variabl

ABSTRACT

Complete integral:

w = aC1z + (C2e-ax – bC1)y + (k – b2cC21 )x – 2bc a C1C2e

–ax + cC22 2a e

–2ax + C3.

4. ∂w

∂x + ay

∂w

∂y + bz

∂w

∂z + c

( ∂w

∂x

)2 = k.

Complete integral: w = C1x + C2 ln |y| + C3|z| + C4, where C1 + aC2 + bC3 + cC21 = k.