Differential Equations of the First Order but not of the First Degree 4-11
2. y
2
+xyp−x
2
p
2
= 0.
Ans:
()()
21+521–5
––0ycxycx=
3. p
2
−ax
3
= 0.
Ans: 25 (y+c)
2
− 4ax
5
= 0
4. xyp
2
− (x
2
+y
2
) p+xy= 0.
Ans: (x
2
−y
2
−c) (y−cx) = 0
5. x
2
p
2
+xyp− 6y
2
= 0.
Ans: (yx
3
−c) (y−cx
2
) = 0
6. xyp
2
+p(3x
2
− 2y
2
) − 6xy= 0.
Ans: (y−cx
2
) (y
2
+ 3x
2
−c) = 0
7. x
2
p
2
− 2xyp+y
2
=x
2
y
2
+x
4
.
Ans: y
2
−x
2
sinh
2
(x+c) = 0
8. yp
2
+ (x−y)p−x= 0.
Ans: (y−x−c) (x
2
+y
2
−c
2
) = 0
9. x
2
p
2
− 2xyp+ 2y
2
−x
2
= 0.
Ans:
(
)
–1
sin± log
⎛⎞
=
⎜⎟
⎝⎠
y
cx
x
10. x+yp
2
= (1 +xy) p.
Ans:
()
2
0
2
x
y
yecxc
−
⎛⎞
−−−=
⎜⎟
⎝⎠
4.2 EQUATIONS SOLVABLE FOR y
Suppose the ...
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