Question

Solve the differential equation y’’= i+(y’)2.

Answer 1

Answer:

xy

dx

dy

−y

2

−x

3

=0

put y

2

=k⇒y

dx

dy

=

2

1

dx

dk

∴ given differential equation becomes

dx

dk

+k(−

x

2

)=2x

2

I.F.=e

∫−

x

2

dx

=

x

2

1

∴ solution is k.

x

2

1

=∫2x

2

.

x

2

1

dx+λ

y

2

−2x

3

=λx

2

take λ=−c (integration constant).