# differential equations

posted by .

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

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

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

• differential equations -

dy/dx=(9+20 x)/(xy^2)

## Similar Questions

1. ### Calculus - Seperable Equations

Solve the separable differential equation (dy/dx)=y(1+x) for y and find the exact value for y(.3). dy/dx = y(1+x) dy/y = (1+x)dx Integral (dy/y) = Integral (1+x)dx ln (y) = x + (1/2)x^2 + C y = e^(x + (1/2)x^2 + C) y(0.3) = e^(0.345 …
2. ### algebra

1)What is the 4x^2=y^2+8y+32 answer= either hyperbola or parabola 2)The graph of which equation is a circle?
3. ### Computer Science - MATLAB

thanks mathmate. It's way above my head to. I got another question Consider the following two equations: x^2 + y^2 = 42 x + 3y + 2y^2 = 6 Define a symbolic equation for each, and solve it by using MATLAB's symbolic capability. Could …
4. ### algebra

solve the exponential equation Express in exact form. 5e^xlog_9 = 11 Is x = (ln11-ln5/log_9 exact form?
5. ### Differential Equations

x dy/dx + y = 1/y^2, solve using bernoulli's equation. i got to du/dx + (2u)/x = 2x(u)^(-1/2). the u^(-1/2) is obviously a problem if im going to solve it using an integrating factor. if that is not what you yourself have gotten to …
6. ### math

solve the equations by finding the exact solution this is question from log 3=x-3
7. ### mathematics

Solve the differential equation x^2dy+ (x-3xy + 1)=0
8. ### PLEEEEEAAAASE HELP WITH DIFFERENTIAL EQ PROBLEMS!!

1) What are the equilibrium solutions to the differential equation and determine if it is stable or unstable with the initial condition y(-4)=1: 0.1(y+2)(4-y) 2) Use Euler's method with step size=0.5 and initial condition y(0)=3 to …
9. ### Differential equation (urgent pls!!!)

Reduce the differential equation below to an exact equation (X - 2siny + 3)dx -(4siny - 2x + 3)dy=0. The problem here is how to solve for the integrating factor...any help pls?