def pde_1st_linear_constant_coeff_homogeneous(eq, func, order, match, solvefun):
 f = func.func
 x = func.args[0]
 y = func.args[1]
 b = match[match['b']]
 c = match[match['c']]
 d = match[match['d']]
 return Eq(f(x, y), (exp((((- S(d)) / ((b ** 2) + (c ** 2))) * ((b * x) + (c * y)))) * solvefun(((c * x) - (b * y)))))

def pde_1st_linear_constant_coeff_homogeneous ( eq , func , order , match , solvefun ) : f = func . func x = func . args [ 0 ] y = func . args [ 1 ] b = match [ match [ 'b' ] ] c = match [ match [ 'c' ] ] d = match [ match [ 'd' ] ] return Eq ( f ( x , y ) , ( exp ( ( ( ( - S ( d ) ) / ( ( b ** 2 ) + ( c ** 2 ) ) ) * ( ( b * x ) + ( c * y ) ) ) ) * solvefun ( ( ( c * x ) - ( b * y ) ) ) ) )
solves a first order linear homogeneous partial differential equation with constant coefficients .