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Eliminate the arbitrary constants.


y = x + Aex + Be-2x

Find the integral surface of (x-y)(p-q) = z(q+1) which contains the circle z=4; x2+y2=42.


Y"+4y'-y=14+6e2x
Obtain the differential equation from the given general solution.

y= c1 cos(4x) +c2 sin(4x) +c3 xcos4x +c4x sin(4x)

Find the integral surface of (x-y)(p-q) = z(q+1) which contains the circle z=4; x2+y2=42.


Obtain a family of solutions for the homogeneous differential equation

what is the differential equation having a solution y=cx²+cx?


Solve the following bvp by eigenfunction expansion method.

y''+2y=2-4x, y(0)=0, y(1)+y'(1)=0


uxx=4ut , 0<x<2 , t>0

u(0,t)=5, u(2,t)=10, t>0

u(x,0)=x, 0≤x≤2

Find the transient and steady-state temperature of the above bvp of heat equation


y=C1e^2x + C2e^-x