Question

solve x⁴d³y/dx³+2x³d²y/dx²-x²dy/dx+xy=1​

Answer 1

Step-by-step explanation:

We have, x

2

dx

dy

−xy=1+cos

x

y

=2cos

2

2x

y

⇒sec

2

(

2x

y

).[x

2

dx

dy

−xy]=2

⇒

2

1

sec

2

(

2x

y

).

x

2

x

dx

dy

−y

=

x

3

1

⇒

dx

d

(tan

2x

y

)=

x

3

1

Integrating, we get

⇒∫

dx

d

(tan

2x

y

)dx=∫

x

3

1

dx

⟹tan

2x

y

=c−

2x

2

1

, which is required solution.

Answer 2

Step-by-step explanation:

x⁴d³-+2x³d²-x²d+xy=1+x/x