Question

Solve the Differential Equation


2
2 − (2 − 1)

+ ( − 1) = 0

Answer 1

Answer:

Using the equation-

dx

dy

+Py=Q

The solution is given by -

y(I.F)=∫Q(I.F)dx

where integration factor=I.F=e

∫Pdx

Here,

dx

dy

−

1+x

2

2x

y=x

2

+1

P=

1+x

2

−2x

and Q=1+x

2

∫Pdx=∫

1+x

2

−2x

dx=∫

z

−dz

dz

where z=x

2

+1⟹dz=2xdx

=−logz=log

z

1

=log

1+x

2

1

I.F=e

∫Pdx

=e

log

1+x

2

1

=

1+x

2

1

Required solution is-

y×

1+x

2

1

=∫(x

2

+1)×

1+x

2

1

dx=∫dx=x

⟹y=x(x

2

+1)+c