Differential Equations Answers

Find the integral surface of the linear partial differential equation
x(y2+z)p-y(x2+z)q=(x2-y2)z,
which contains the straight line x+y=0 , z=1 .

Find the envelope of the family of spheres with centre (l,m,o) and radius one . Also obtain the equation of the characteristic curve of the family when l=m .

Find the differential equation of the space curve in which the two families of surfaces ax2+by2+cz2=u and a2x2+b2y2+c2z2=v intersect .

Solve the differential equation xdy-(3y+x5(y)1/3)dx=0 .

Solve : xy'-y=(e)y' . Also obtain its singular solution.

Solve the differential equation:
(x y2 -x2)dx + (3x2y2+x2y-2x3+y2)dy=0 .

solve the differencial equation:
y sin 2x dx= (1+y2+(cos)2 x)dy.

Solve the differencial equation y" = 1+(y')2.

A mass weighing 39.5 kg. streches a spring 1/4m. At t=0 , the mass is released from a point 3/4m below the equilibrium position with an upward velocity of (5/4)m/sec. Determine the function x(t) that describes the subsiquent free motion.

Solve : xy' - y =e to the power y'. Also obtain its singular solution.