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Q. show that u(x, y)=xf(2x+y) is a general solution of x∂u/∂x-2x ∂u/∂y=u
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
Q. form the partial differential equation by eleminating 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
Q. form the partial differential equation by eleminating the arbitrary function from the relation
u=f(x-3y)+g(2x+y)
u=f(x-3y)+g(2x+y)
Q. form the partial differential equation by eleminating the arbitrary function from the relation
u=xnf(y/x)
u=xnf(y/x)
Q. form the partial differential equation by eleminating the arbitrary function from the relation
u=y2+2f(1/x+ln y)
u=y2+2f(1/x+ln y)
Q. Obtain the partial differential equation by eleminating 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
Q. Obtain the partial differential equation by eleminating the arbitrary constant from the relation
u=aeby+sinbx
u=aeby+sinbx
Q. Obtain the partial differential equation by eleminating the arbitrary constant from the relation
u=xy+y√(x^2-a^2 )+b
u=xy+y√(x^2-a^2 )+b
Q. Obtain the partial differential equation by eleminating the arbitrary constant from the relation
u=ax+(1-a)y+b
u=ax+(1-a)y+b
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#340153 on Dec 2023
#340153 on Dec 2023