Discuss the following partial differential equations regardi

Discuss the following partial differential equations regarding their properties (linearity, order, coefficients, number of variables, homogeneity and basic type) u_t = u_xy + u 5u_y 4u_xt + u_tt = -u_xx + tan(t) u_tt = UU_xxxx + e^-t xu_x - 4yu_y + u^2 = 0

Solution

(a)

Non-linear; Order- 2; Coefficients- 1, -1, -1, -5; Variables- u, x, y

(b)

Non-linear; Order- 2; Coefficients- 4, 1, 1, -1; Variables- u, x, t

(c)

Non-linear; Order- 4; Coefficients- 1, -1, -1; Variables- u, t, x

(d)

Linear; Order- 1; Coefficients- 1, -4, 1; Variables- x, y, u