Differential Equations Answers

According to Newton’s law of cooling, the rate at which a substance cools in moving
air is proportional to the difference between the temperature of the substance and that
of the air. If the temperature of the air is C
o
290 and the substance cools from
C
o
370 to C
o
330 in 10 minutes, find when the temperature will be C
o
295 .

Solve: dy/dx + y = y^3(cosx - sinx)

Solve: dy/dx + ylogy/x = y(logy)^2/x^2

Solve : dy/dx + y/x = y^2/x^2

Solve: dy/dx + 2xy= e^-x^2

Solve: x^2y^2(2ydx + xdy) - (5ydx + 7xdy)=0

Show that the Integrating factor of the equation (x^2+y^2+2x)dx + 2ydy=0 is e^x and its particular solution is x^2 + y^2=2e^1-x when x=y=1

Solve: (3ydx - 2xdy) + x^2y^-1(10ydx - 6xdy)=0

Solve: 2siny^2dx + xycos^2dy=0 ,
Given: y(2)=√π/2