differential equations

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:)

  1. 👍 0
  2. 👎 0
  3. 👁 385
  1. dy/dx=(9+20 x)/(xy^2)

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. ALGEBRA 1!PLZ HELP!

    Use the Substitution method to solve the system of equations. y - 2x = -5 3y - x = 5 Solve the first equation for y. y = 2x-5 Substitute that for y in the second equation and solve for x. Then use the value of x to substitute back

  2. College Algebra

    1. Find the domain of the composite function f o g. f(x)= 2/x-3; g(x)= 7/x 2. Solve the following exponential equation. Exact answers only. 2^1-9x = e^2x

  3. Algebra

    98. Solve the equation -49 = x - 50 x=1? 94. Determine if the following equation is a function: x=2 No? 92. Determine if the following equation is a function: y=5 No? 89. Solve for x in the equation: 6/7x - 6 = -2 I got x=28/3 86.

  4. 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?

  1. Trignometry questions EASY HELP

    1. Which is a solution to the equation below? sin2xsecx=1 2. What is the exact value of cos15 degrees? 3. Which expression is equivalent to the expression below? cos^2 xsin^2? 4. What is the exact value of cos2theta? one side is 8

  2. quadratic equations

    can you solve the equation using the quadratic formula x2 + 3x = 7? Explain and provide an exact answer.

  3. calculus

    Having a really hard time with this! e^8x^2-5 = 14 solve the exponential equation express in exact form. Someone please help!

  4. College Algebra

    "Solve each equation. Round your answers to the nearest ten-thousandth." (These are my directions) Here is the equation: 3^n + 9 = 69 How do I solve this getting the answer asked for?

  1. math

    Solve the equation by completing the square. If the solutions are real, give exact and approximate answers. Otherwise, list the exact solutions. 7x^2-4x+1=2x^2-7x+3 Please help!!!!! :(

  2. math

    Angles x and y are located in the first quadrant such that sinx=3/5 and cosy=5/13. a) Determine an exact value for cosx b) Determine an exact value for siny

  3. math

    Let f(x)= π^2 and g(x) = e^x. Then solve the following equation and give answer(s) in exact form: f(x-1)-2∙g(2x-1)=0

  4. math

    What is the first step in solving the linear system {2x − 3y = 11 {−x + 5y = −9 by the substitution method in the most efficient way? A. Solve the first equation for x. B. Solve the first equation for y. C. Solve the second

You can view more similar questions or ask a new question.