Differential Equations Answers

Solve the differential equation of the following non-exact differential equation. Show complete solution.

(y - xy)dx + xdy = 0

_d²_y/dx²_{-4 dy/dx+4y=o}

4 d²y/dx²+25y=0

d²y/dx²+5 dy/dx+4y=0

A loaded boat weighs 981kg.The force exerted upon the boat in the direct of motion by the oars,is equivalent to a constant force of 15N and the resistance in Newton to the motion is equal to twice the speed of the boat . If th boat starts from rest, determine;

(i)the limiting speed

(ii)speed at the end of 10 sec.

Equation of Rectangular Curves.

1. For a certain curve, the point of contract of each tangent to its bisects the part of the tangent terminating on the coordinate axes. Find the equation of the curve.

2. The area bounded by the curve, the x axis, a fixed ordinate and a variable ordinate is proportional to the difference between the ordinates. Find the equation of the curve.