exactly one function math display block frac partial u partial x frac partial u partial math ''x'' ''g'' ''x'' values even phenomena possible instance following pde arising naturally field differential geometry illustrates example simple completely explicit solution formula free choice three numbers even one function function math display block frac partial partial x frac frac partial u partial x sqrt left frac partial u partial x right left frac partial u partial right frac partial partial frac frac partial
Formal science Mathematics Pure mathematics Analysis Partial differential equations