A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

solve the DE: dy/dx=-(y^3 +(4e^x)y)/2e^x + 3y^2)

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can anyone help? i am stuck at trying the separation of variables

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    want variables for d and e right?

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well separation of variables would be to the the dx and all x's on one side and the dy and all y's on the other

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (dy)/(dx)=-(y^(3)+(4e^(x))*y)/(2)*e^(x)+3y^(2) Multiply each term in the equation by d. (dy)/(dx)*d=(-(y^(3)+(4e^(x))*y)/(2)*e^(x)+3y^(2))*d Simplify the left-hand side of the equation by canceling the common terms. (dy)/(x)=(-(y^(3)+(4e^(x))*y)/(2)*e^(x)+3y^(2))*d Simplify the right-hand side of the equation by simplifying each term. (dy)/(x)=-(dy(y^(2)e^(x)+4e^(2x)-6y))/(2) Multiply each term in the equation by x. (dy)/(x)*x=-(dy(y^(2)e^(x)+4e^(2x)-6y))/(2)*x Simplify the left-hand side of the equation by canceling the common terms. dy=-(dy(y^(2)e^(x)+4e^(2x)-6y))/(2)*x Simplify the right-hand side of the equation by simplifying each term. dy=-(dxy(y^(2)e^(x)+4e^(2x)-6y))/(2) Multiply each term in the equation by 2. dy*2=-(dxy(y^(2)e^(x)+4e^(2x)-6y))/(2)*2 Multiply dy by 2 to get 2dy. 2dy=-(dxy(y^(2)e^(x)+4e^(2x)-6y))/(2)*2 Simplify the right-hand side of the equation by simplifying each term. 2dy=-dxy(y^(2)e^(x)+4e^(2x)-6y) Multiply -dxy by each term inside the parentheses. 2dy=(-dxy^(3)e^(x)-4dxye^(2x)+6dxy^(2)) Remove the parentheses around the expression -dxy^(3)e^(x)-4dxye^(2x)+6dxy^(2). 2dy=-dxy^(3)e^(x)-4dxye^(2x)+6dxy^(2) Since d is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation. -dxy^(3)e^(x)-4dxye^(2x)+6dxy^(2)=2dy Since 2dy contains the variable to solve for, move it to the left-hand side of the equation by subtracting 2dy from both sides. -dxy^(3)e^(x)-4dxye^(2x)+6dxy^(2)-2dy=0 Factor out the GCF of -dy from each term in the polynomial. -dy(xy^(2)e^(x))-dy(4xe^(2x))-dy(-6xy)-dy(2)=0 Factor out the GCF of -dy from -dxy^(3)e^(x)-4dxye^(2x)+6dxy^(2)-2dy. -dy(xy^(2)e^(x)+4xe^(2x)-6xy+2)=0 If any individual factor on the left-hand side of the equation is equal to 0, the entire expression will be equal to 0. -dy=0_(xy^(2)e^(x)+4xe^(2x)-6xy+2)=0 Set the first factor equal to 0 and solve. -dy=0 Divide each term in the equation by -1y. -(dy)/(-1y)=(0)/(-1y) Simplify the left-hand side of the equation by canceling the common terms. d=(0)/(-1y) Any expression with zero in the numerator is zero. d=0 Set the next factor equal to 0 and solve. (xy^(2)e^(x)+4xe^(2x)-6xy+2)=0 Remove the parentheses around the expression xy^(2)e^(x)+4xe^(2x)-6xy+2. xy^(2)e^(x)+4xe^(2x)-6xy+2=0 Take the natural logarithm of both sides of the equation to remove the variable from the exponent. ln(xy^(2)e^(x)+4xe^(2x)-6xy+2)=ln(0) The logarithm of 0 is undefined. Undefined Since the logarithm is undefined, there is no solution. No Solution The final solution is all the values that make -dy(xy^(2)e^(x)+4xe^(2x)-6xy+2)=0 true. d=0

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i am completely lost with what you did

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i am telling you how to get each variable

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its differential equations so i am only solving for y in the end

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay so need y

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    dy/dx= 2-e^x/ 3+2y this can be done using variable separable method; collect x and dx terms along one side and y and dy terms along other side hence (3+2y)dy= (2-e^x)dx integrating both sides 3y +2y^2/2 = 2x - e^x +c 3y+y^2= 2x-e^x+c so now y^2+3y -2x+e^x=c ------A is the solution where c is the integrative constant in next question do you want to find max value for dy/dx or y if you want to find max value for y then equate dy/dx =0 so 2-e^x/3+2y=0 2-e^x=0 e^x=2 ==> x= log 2 now the intervals ae -infinity to log2 and log2 to infinity now substitute values in between -ve inf to log2 in A and check if it is less than 0 then that value is max else it is max sim do for the values between log2 to infinty

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    dy/dx = (2 - e^x)/(3 + 2y) (3 + 2y) dy = (2 - e^x) dx Integrating both sides: 3y + y² = 2x - e^x + C (y + 3/2)² = 2x - e^x + C y = +/-√(2x - e^x + C) - 3/2

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    maybe this will clear it up some

  12. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.