Differential Equations Answers

2 The differential equation for the curve given by the segment joining point Q(x,y) and the point of intersection of the normal at Q with the x –axis is bisected by the y –axis is given by

(a) 2y+x dx/dy=1/2y


(b) y+x dx/dy =1/2y

© y+x dx dy=1 3y

(d) y+3x dx/dy=1/2y
4 For a particular element the rate of change of temperature(T) with respect to volume (V) is proportional to the vapor temperature and inversely proportional to the square of the volume, this phenomenon as a differential equation is

(a) dT/dV=kT/V^2


(b) dT/dV=kT/2V^2

© 2 dT/dV=kT/V^3

(d) dT/dV=3 kT/V^2

8. Solve
y(xy+1)dx+x(1+xy+x^2y^2)dy=0

9. Solve
xdy−ydx−√x^2−y^2 dx=0

10 The population of student P at NUN increases at a rate proportional to the population and to the addition of 150,250 and the population divided by 3, the differential equation of this statement is

5 Derive the differential equation for the area bounded by the arc of a curve, the x- axis, and the two ordinates, one fixed and one variable, is equal to trice the length of the arc between the ordinates
6 Find the differential equation of all straight lines at a unit distance from the origin
7 Obtain the differential equation associated with the given primitive
lny=Ax^2+B
, A and B being arbitrary constants.

1 H grams of artificial sugar in water are being converted into dextrose at a rate which is proportional to the square of the amount unconverted. Find the differential equation expressing the rate of conversion after v minutes given that s grams is converted in v minutes and c being the constant of proportionality.
2 A vehicle of mass m moves along a straight line ( the – axis) while subject to a force indirectly proportional to its displacement x from a fixed point O in its path and 2) a resisting force proportional to its acceleration. Express the total force as a differential equation.
3 Derive the differential equation associated with the primitive
y=Ax^3+Bx^2+Cx+D
where A, B, C and D are arbitrary constants.

1. Solve
(x^3+y^3)dx−3xy^2dy=0

2. Solve the variable separable
x^3dx+(y+1)^2dy=0

3. Solve
(1+2e^x/y)dx+2e^x/y(1−x/y)dy=0

4. Solve
y(xy+1)dx+x(1+xy+x^2y^2)dy=0

5. Solve
xdy−ydx−√x^2-y^2 dx=0

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Find the general solution the differential equation
y''-3y'=8*exp(3x)+4sinx

Solve the intital value problem
(cosy)dy/dx-siny=x,y(0)=0

Find the general solution of the following differential equation
y''-4y'+3y=2*exp(x)*(1+2x)+x

y'''+y''=8x^2