0.1 Equations di érentielle du premier ordre - HEH

y√1−x2+ = 0
y0+ycos x= 0
yy0= cos2x
y2y0+x2= 0
x(x−1)y0−y(y−1) = 0
y−xy0=x2
y
x2+y2−2x2y0= 0
xy0−y=px2+y2
2xyy0= 3y2+x2
xy0−2y+ 3x= 0
y0−y= 1 −x
y0−4y= 2x−4x2
y0= 2x(y−x)+1
y0−3y= sin(2x)
xy0+ 2y= expx
xy0−y=ln|x|+x2
3xy0−2y=x2cos x
√y
xy0+y=y2lnx
x2y0−xy +y2= 0
xy0=y2−3xy −1
y−2xy0=y02
y= 1 + 2xy0+y02
yp1 + y02=x+yy0
xy02−2yy0−x= 0
y=−xy0−ln(y0)
y−xy0=y03
y=xy0+y0−y02
y=xy0+y0ln(y0)

y” + y0+y=x2+x+ 1
y”+2y0+y= 2 exp−x
y(0) = 3 y0(0) = 1
y”−3y0−4y=xexp|x|
y”+2y0+ 5y= exp−x(2 cos(2x)−3 sin(2x))
y”+4y0+ 4y=exp−2x
1 + x2
x2y”−3xy0+ 4y=x2
y=x2
x2y” + xy0−4y= 4x2
y” + ω2y= cos(ax)
a6=ω a 6=−ω
a=ω a =−ω
y”−2y0+y= 5 cos(x−π
4)
y(0) = 0 y0(0) = 0
y”+4y+ sin(2x) = 0
y(π)=1 y0(π) = 1