WorksheetsFirst Order Linear Differential Equations
Total questions: 10
Worksheet time: 12mins
Which of the following differential equations is not linear?
dxdy+xy2=ex
x1dxdy−y=x+1
xdxdy+y=x−x2y
dxdy=1−xy
The general solution of the differential equation
dxdy=2xy
is
y=ex2+A
y=Aex2
y=ex2
y=ln(x2+A)
The particular solution of the differential equation
dxdy=y2e2x
for which y=1 when x=0 is given by
y=3−e2x2
y=1+e2x2
y=2−e2x1
y=e−2x
An integrating factor of the differential equation
dxdy−x2y=3x2
is
e−2x
−ln(x2)
x2
x21
An integrating factor of the differential equation
(e2x+1)dxdy+4e2xy=x
is
e2x+1
e2e2x
(e2x+1)2
(e2x+1)4
The general solution of the differential equation
dxdy−(cotx)y=sin(2x)
is
y=21sin(2x)+Asinx
y=2sin2(x)+sinx+A
y=32sin2(x)+Acosec(x)
y=2sin2(x)+Asinx
The general solution of the differential equation
xdxdy+3y=x2
is
y=5x2+x3c
y=x2+Cx
y=5x+C
y=2x2+xc
The particular solution of the differential equation
dxdy+2y=x
for which y=0 when x=0 is given by
y=21x2e−2x
y=4e−2x+2x−1
y=1−e−2x
y=21−e−2x
The particular solution of the differential equation
(x2+1)dxdy+xy=x(x2+1)
for which y=0 when x=0 is given by
y=31(x2+1)23−31
y=4(x2+1)x2(x2+2)
y=31(x2+1)−31(x2+1)−21
y=31(x2+1)+31(x2+1)21
The general solution of the differential equation
dxdy+y=2e−x
is
y=e−x(A+2x)
y=Ae−x+2e−x
y=Aex+2xe−x
y=Ae−x+Bxe−x
