Differential Equations Answers

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

6 Solve
(x3+y3)dx−3xy2dy=0
x5−2y3=Cx
x3−2y3=Cx
x3−3y3=Cx
x3−2y2=Cx

7 Solve
(1+2exy)dx+2exy(1−xy)dy=0
5x+2yexy=C
x+2ye2xy=C
x+2yexy=C
5x+3yexy=C

8 Solve
y(xy+1)dx+x(1+xy+x2y2)dy=0
2x2y2lny−2xy−1=Cx2y2
3x2y2lny−2xy−3=Cx2y2
2x2y2lny−xy=Cx2y2
2x3y2lny−2xy−1=Cx2y5

9 Solve
xdy−ydx−x2−y2−−−−−−√dx=0
Cx=2earcsinyx
Cx=earcsinyx
Cx=earcsin2y3x
Cx=earccosyx

10 The population of student P at NOUN 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
dPdT=3kP(150,250+P)4
dPdT=2kP(150,250+P)3
5dPdT=kP(150,250+P)3
dPdT=kP(150,250+P)3