find the partcular solution of the differential equation dy/dx + y tanx = 3x^2 + x^3 tanx
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Answer:
) (x
2
+y
2
)dx+2xydy=0
dx
dy
=
2xy
−(x
2
+y
2
)
dx
dy
=
2(
x
y
)
−(1+(
x
y
)
2
)
x
y
=u⇒
dx
dy
=u=x
dx
du
u=
dx
xdu
=
24
−(1+4
2
dx
xdu
=
24
−(1+4
2
)
–4=
24
−1−4
2
−24
2
dx
xdu
=
24
−1−34
2
∫
1+34
2
24
du=−∫
x
dx
∫
1+3t
dt
=−∫
x
dx
3
1
ln(1+3t)=−ln(x)+ln(c)
3
1
ln(1+3t)=+ln(
x
C
)
3
1
ln(1+3x
2
)=ln(
x
c
)
(1+3x
2
)
1/3
=(
x
C
)
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