Help Solving ODE: 5x2y2 - 2x3y2 = 1

[b3n5p34km4n]

so I'm in my second week of my first differential equations class, and i can't seem to get this problem.

Show that 5x²y² - 2x³y² = 1 is an implicit solution of the differential equation x(dy/dx) + y = x³y³ on the interval 0 < x < 5/2

for dy/dx, i got (3xy-5y)/(5x-4x²), I'm pretty sure it's right, but if it's not then it might be why i can't quite get this. i also solved for y explicitly, but then i realized i could just factor it out.

well that's what i did, and all i end up with is just a big polynomial... I'm sure I'm doing it wrong. help please?

edit: alright alright i just saw the sticky... truth be told i just google differential equations forum and signed up real quick to post this, so i was in a hurry. sorry i posted this is the wrong forum :(

 

[HallsofIvy]

so I'm in my second week of my first differential equations class, and i can't seem to get this problem.

Show that 5x²y² - 2x³y² = 1 is an implicit solution of the differential equation x(dy/dx) + y = x³y³ on the interval 0 < x < 5/2

for dy/dx, i got (3xy-5y)/(5x-4x²), I'm pretty sure it's right, but if it's not then it might be why i can't quite get this. i also solved for y explicitly, but then i realized i could just factor it out.

No, that derivative is not right. Just use "implicit differentiation" to get $10xy^2dx+ 10x^2ydy- 5x^2y^2dx- 4x^3y dy= 0$. Rearrange those to $(10xy^2- 5x^2y)dx+ (10x^2y- 4x^3y)dy= 0$. That, now, is the same as $dy/dx= -(10xy^2- 5x^2y)/(10x^2y- 4x^3y)$. Factor and reduce that.

well that's what i did, and all i end up with is just a big polynomial... I'm sure I'm doing it wrong. help please?

edit: alright alright i just saw the sticky... truth be told i just google differential equations forum and signed up real quick to post this, so i was in a hurry. sorry i posted this is the wrong forum :(