Differential Equations Answers

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Solve the simultaneous differential equation
dx/x^2-y^2-z^2=dy/2xy=dz/2xz
(D-D'+2)(D+D'-1)=e^x-y -x^2y

p^2q^2+x^2y^2= x^2q^2(x^2+y^2)


A bar 40cm long with insulated sides had its ends A and B maintained at 0 degree and 100 degree Until steady state condition prevails Then the temperature at A is suddenly raised to 20 degree and at the same time that of B is lowered to 60 degree. Find the temperature distribution in the bar at time t
Show that the differential equation

2xz + q^2 = x(xp + yq)

has a complete integral


z+ a^2x = axy + bx^2

and deduce that

x(y + hx)^2 = 4(z - kx^2)

is also a complete integral.
Check the condition of integrability & solve

yzdx + 2xzdy − 3xydz = 0.

y′′′−2y′′−y′+2y=e4x


variation of paramaters


Solve : (D^2-2D+4) y=8x^2e^2x sin2x
Solve : d2y/dx2+a2y=sec ax
Solve : (x^3+xy^2+a^2y) dx+(y^3+yx^2+a^2x) dy=0
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