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Calculus
Q. show that u(x, y)=xf(2x+y) is a general solution of x∂u/∂x-2x ∂u/∂y=u
Calculus
Q. show that u(x, t)=e-8tsin2x is a solution to the initial boundary value problem
∂u/∂t=2(∂^2 u)/〖∂x〗^2
(B.c,s) u(0,t)=0, u(π, t)=0 t>0
(I.C) u(x,0)=sin2x
∂u/∂t=2(∂^2 u)/〖∂x〗^2
(B.c,s) u(0,t)=0, u(π, t)=0 t>0
(I.C) u(x,0)=sin2x
Calculus
Q. form the partial differential equation by eliminating the arbitrary function ᵩ
from the relation
ᵩ(x+y+u, x2+y2+u2)=0
from the relation
ᵩ(x+y+u, x2+y2+u2)=0
Calculus
Q. form the partial differential equation by eliminating the arbitrary function from the relation
u=f(x-3y)+g(2x+y)
u=f(x-3y)+g(2x+y)
Calculus
Q. form the partial differential equation by eliminating the arbitrary function from the relation
u=xnf(y/x)
u=xnf(y/x)
Calculus
Q. form the partial differential equation by eliminating the arbitrary function from the relation
u=y2+2f(1/x+ln y)
u=y2+2f(1/x+ln y)
Calculus
Q. Obtain the partial differential equation by eliminating the arbitrary constant from the relation
x^2/a^2 +y^2/b^2 +u^2/c^2 =1
x^2/a^2 +y^2/b^2 +u^2/c^2 =1
Calculus
Q. Obtain the partial differential equation by eliminating the arbitrary constant from the relation
u=aeby+sinbx
u=aeby+sinbx
Calculus
Q. Obtain the partial differential equation by eliminating the arbitrary constant from the relation
u=xy+y√(x^2-a^2 )+b
u=xy+y√(x^2-a^2 )+b
Calculus
Q. Obtain the partial differential equation by eleminating the arbitrary constant from the relation
2u=x^2/a^2 +y^2/b^2
2u=x^2/a^2 +y^2/b^2
