Question

Verify that y1=x is one solution of (1-x2)y’’(x)-2xy’(x)+2y(x)=0 and find its general solution

Answer 1

Step-by-step explanation:

Correct option is

C

ln(xy)=x+2y+C

xy

′

(2y−1)=y(1−x)

By separation of variables , we get (

y

2y−1

)dy=(

x

1−x

)dx

⇒2dy−

y

1

dy=

x

1

dx−dx

Apply integration on both sides , we get ∫2dy−∫

y

1

dy=∫

x

1

dx−∫dx

⇒2y−lny=lnx−x+C

⇒ln(xy)=x+2y+C

Answer 2

Answer:

ya it is correct man