# 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

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

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

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

1. 👍 0
2. 👎 0

## 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

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