Find a general solution to each first - degree ordinary differential equation. If an initial condition is given, find the corresponding particular solution. Write all solutions explicitly if possible. Solve all a.
(dr)/(d\theta )=(r^(2))/(\theta )
b.
y^(')=(1-y)cos(x),y(\pi )=2
c.
2xy(dy)/(dx)=4x^(2)+3y^(2)
d.
(9x^(2)+y-1)dx-(4y-x)dy=0,y(1)=0
e.
(dy)/(dx)=ry-ky^(2),
where
r
and
k
are constants,
r>0
f.
(dx)/(dt)=\sqrt(x+t+1)
g.
(3xy+y^(2))+(x^(2)+xy)y^(')=0

Question

Find a general solution to each first - degree ordinary differential equation. If an initial condition is given, find the corresponding particular solution. Write all solutions explicitly if possible. Solve all a.

(dr)/(d\theta )=(r^(2))/(\theta )

b.

y^(')=(1-y)cos(x),y(\pi )=2

c.

2xy(dy)/(dx)=4x^(2)+3y^(2)

d.

(9x^(2)+y-1)dx-(4y-x)dy=0,y(1)=0

e.

(dy)/(dx)=ry-ky^(2),

where

r

and

k

are constants,

r>0

f.

(dx)/(dt)=\sqrt(x+t+1)

g.

(3xy+y^(2))+(x^(2)+xy)y^(')=0

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