Posted by **allison** on Wednesday, October 8, 2008 at 3:03pm.

the directions are to determine whether or not the equation is exact if so then solve it.

the question is (x-y^3+ysinx)dx = (3xy^2+2ycosx)dy

i solve and i got that it is exact

because

My is -3y^2+2ysinx and Nx is -3y^2+2ysinx

since m and n are equal then they are exact

then i started with M

integral of (x-y^3+y^2sinx)dx + g(y)

it got x^2/2 -xy^3-y^2cosc + g(y)

then i took derivative of it wrt y

-3xy^2-2ycosx + g'(y) = N

then -3xy^2 + integral g'(y)= integral of -3xy^2 dy

then g(y) = xy^3 -xy^3 +c

then i got

f(x,y)= 1/2x^2 - xy^3-ycosx+xy^3 = c

but when i check the back of the book

their answer was

xy^3+y^2cosx-1/2x^2 =c

are the same or did i do something wrong...

please help me understand my mistake

anyone please

thanks in advance:)

- differential equations -
**James**, Friday, September 9, 2011 at 12:02am
dy/dx=(9+20 x)/(xy^2)

## Answer This Question

## Related Questions

- Calculus - Seperable Equations - Solve the separable differential equation (dy/...
- Computer Science - MATLAB - thanks mathmate. It's way above my head to. I got ...
- Differential equation (urgent pls!!!) - Reduce the differential equation below ...
- algebra - 1)What is the 4x^2=y^2+8y+32 answer= either hyperbola or parabola 2)...
- PLEEEEEAAAASE HELP WITH DIFFERENTIAL EQ PROBLEMS!! - 1) What are the equilibrium...
- math - solve the equations by finding the exact solution this is question from ...
- mathematics - Solve the differential equation x^2dy+ (x-3xy + 1)=0
- Differential Equations - x dy/dx + y = 1/y^2, solve using bernoulli's equation. ...
- algebra - solve the exponential equation Express in exact form. 5e^xlog_9 = 11 ...
- pre-calculus - solve the equation 1. In x + In (x+12) =2 x= ? or either there is...

More Related Questions