Differential Equations Answers

solve

2 (x^2 + xy) dx + (x^2 + y^2) dy = 0

Find the temperature distribution in a bar of length 10 cm, which is perfectly insulated along its length, whose ends are kept at 0 degree C and whose initial temperature distribution is given by,
t(x)=x for 0<x<5
=10-x for 5<x<10

A mass of 10 kg suspended from a spring stretches the spring by 8 cm. The upper end of the spring is then given a motion of (sin 2t + cos 2t) m. Find the equation of motion of the mass.

A body of mass m falls from rest in a medium in which the resistance is proportional to the velocity. If the density of the medium is one fourth that of the body and its terminal velocity is 8 m/s
, find the velocity at the end of 3 s and the distance traveled in that time.

Find the two Frobenius series solutions for the following differential equation:x^2d2y/dx2+6xdy/dx+(6-x^2)y=0

y''+2y'+24y=16-(x+2)e^4x

y' = x^2 + y^2
y(0) = 1