Can someone check a couple of these?

[hbomb]

Are these the correct answers for the following questions?

1 Solve the Bernoulli equation.

a) [tex]x\frac{dy}{dx}+67=3xy^\frac{4}{3}[/tex]

What I got:
[tex]\frac{1}{y^\frac{1}{3}}=x+cx^2[/tex]


b) [tex]x^2y'+2xy=5y^4[/tex]

What I got:
[tex]2y^(-3)=\frac{30}{13}\frac{1}{x}+cx^12[/tex]


2 Solve each differential equation.

a) [tex]xy''+2y'=6x[/tex]

What I got:
I let u=y', y''=du/dx
[tex]y=x^2-\frac{c_1}{x}+c_2[/tex]

b) [tex]y^3y''=1[/tex]

What I got:
I let u=y', y''=udu/dy
[tex]y=c_1\sqrt{csc(x+c_2)}[/tex]

 

[kurt.physics]

No, these are not correct answers. For the first question, for part a, the correct answer is y = x^3/3 + Cx^2, and for part b, the correct answer is y = (5/13)^(1/3) x^(4/3) + Cx^(-1/3). For the second question, for part a, the correct answer is y = x^2 - c_1/x + c_2, and for part b, the correct answer is y = c_1 csc^(1/2) (x + c_2).