Differential equations assignment T2

[mathi85]

Hi!

I would like to ask anyone with some spare time to check my assignment questions. Last time I was asked to post one task at a time so I will.
Thank you in advance for your time.

Task 2:

Determine the equation of the curve which satisfies the differential equation:

2xy(dy/dx)=x²+1

and which passes through the point (1, 2)

Solution:

2xy(dy/dx)=x²+1 /:2x
y(dy/dx)=(x²+1)/(2x)
y(dy/dx)=(1/2)[(x²+1)/x]

∫ y dy=(1/2)∫ x+(1/x) dx
(1/2)y²=(1/2)(lnx+(1/2)x²)+c

General Solution
(1/2)y²=(1/2)lnx+(1/4)x²+c

x=1 when y=2

∴(1/2)(2)²=(1/2)ln(1)+(1/4)(1)²+c
∴c=7/4

Particular Solution:
(1/2)y²=(1/2)lnx+(1/4)x²+7/4
∴y=√[lnx+x²/2+3.5]

 

[ShayanJ]

Everything seems OK!

 

[mathi85]

Thanks a lot!