Differential Equations Answers

Solve charpit method: 2z+p^2+qy+2y^2=0

The rate of change of temperature of an object is proportional to the difference between

the temperature of the object and its environment. A glass of hot water at a temperature

of 70ºC is kept in a room which is at a temperature of 30 ºC. If after 3 minutes the

temperature of the water is 50 ºC, what will be its temperature after 5 minutes?

Show that the closed sphere with centre (2,3,7) and radius 10 in 3 R is contained in the

open cube P = {(x, y, z) : x − 2 <11, y − 3 <11, z − 7 <11}.

2x(1-x)y"+(1-x)y'+3y=0 solve by forbeinus series.

X^2y"+x(x-1) y'+(1-x)y=0 solve by series solution

(x^2+1) y"+xy'-y=0 solve by power series

(x^2+1) y''+xy'-xy=0 in series solution

A curve is such that dy∕dx=√ (2x+5) and (2,5) is a point on the curve. What is the equation of the curve?

Using the method of undetermined coefficients, find the general solution of the differential equation,

y'''' - 2y''' + 2y'' = 3e^(-x) + 2e^(-x)x + e^(-x)sinx.

a curve is such that dy/dx = -x square + 5x - 4.

1) find the x- coordinates of each of the stationary points of the curve.

2) obtain an expression for d square y/d x square (second derivative) and hence or otherwise find the nature of each of the stationary points .

3)given that the curve passes through the point (6 , 2 ), find the equation of the curve .