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Mathematics
Mathematics
Problem
1. For each of the differential equations given below, indicate its order and degree (if defined). (i) `
d
2
y
d
x
2
+
5
x
(
d
y
d
x
)
2
−
6
y
=
log
x
\frac{d^{2} y}{d x^{2}}+5 x\left(\frac{d y}{d x}\right)^{2}-6 y=\log x
d
x
2
d
2
y
+
5
x
(
d
x
d
y
)
2
−
6
y
=
lo
g
x
` (ii) `
(
d
y
d
x
)
3
−
4
(
d
y
d
x
)
2
+
7
y
=
sin
x
\left(\frac{d y}{d x}\right)^{3}-4\left(\frac{d y}{d x}\right)^{2}+7 y=\sin x
(
d
x
d
y
)
3
−
4
(
d
x
d
y
)
2
+
7
y
=
sin
x
` (iii) `
d
4
y
d
x
4
−
sin
(
d
3
y
d
x
3
)
=
0
\frac{d^{4} y}{d x^{4}}-\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0
d
x
4
d
4
y
−
sin
(
d
x
3
d
3
y
)
=
0
`
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