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solve (1+2xy cos x^2 -2xy)dx+(sinx^2-x^2)d y=0

solve the following bondry value problems by the method of separation of variables

Ut = Uxx 0<x<1 , t>0

U(0,t)= 0 ,U(pi ,t)= 0

U(x , 0) = sinx + 2sin3x


solve (xz-y)p + (yz - x)q =1-z^2
Z^2dx+(z^2-2yz)dy+(2y^2-yz-xz) dz=0

 Find the Fourier Sine transform of f(x) = 1 in   0,l


dx/y^2 z=dy/xz=dz/yz solution ?


2yzdx-2xzdy-(x^2-y^2)(z-1)dz=0
y" — 9y = 0. + e.
A rod of length L has its ends A and B maintained at 20 °C and 40 °C respectively
until steady state condition prevail. The temperature at A is suddenly raised to
50 °C while that at B is lowered to 10 °C and maintained thereafter. Find the
subsequent temperature distribution of the rod.
Y^2+x^2p^2-2xyp=4/p^2
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