Differential Equations Answers

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

Find the integral curves of
1.dx/y(x+y)=dy/x(x+y)=dz/z(x+y)
2.dx/x=dy/y+x²=dz/y+z
3.dx/y-z=dy/z-x=dz/x-y
4.dx/xz-y=dy/yz-x=dz/xy-z
5.dx/y+5z=dy/z+6x=(dz/x+8y)s

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.

Find the complete integral of the differential equation xp(11+q) = (y+z)q

corresponding to that integral of Charpit’s equations which involve only q and x, and deduce that
(z+hx+k )^2 = 4 hx (k - y)

is also a complete integral.

Show that the integral surface of the

equation

z(1- q^2) = 2(px + qy)

which passes through the line x = 1, y = hz + k

has an equation

(y- kx)^2 = z^2 {(1+h^2)x- 1}

Find the integral surface of the differential equation (y+zq)^2 = z^2 (1+p^2+q^2)
circumscribed about the surface x^2 − z^2 = 2y.

Check the condition of integrability & solve

yzdx + 2xzdy − 3xydz = 0.