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anonymous
 5 years ago
solve the DE:
dy/dx=(y^3 +(4e^x)y)/2e^x + 3y^2)
anonymous
 5 years ago
solve the DE: dy/dx=(y^3 +(4e^x)y)/2e^x + 3y^2)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can anyone help? i am stuck at trying the separation of variables

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0want variables for d and e right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.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 lefthand side of the equation by canceling the common terms. (dy)/(x)=((y^(3)+(4e^(x))*y)/(2)*e^(x)+3y^(2))*d Simplify the righthand 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 lefthand side of the equation by canceling the common terms. dy=(dy(y^(2)e^(x)+4e^(2x)6y))/(2)*x Simplify the righthand 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 righthand 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 righthand side of the equation, switch the sides so it is on the lefthand 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 lefthand 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 lefthand 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 lefthand 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am completely lost with what you did

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am telling you how to get each variable

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its differential equations so i am only solving for y in the end

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dy/dx= 2e^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= (2e^x)dx integrating both sides 3y +2y^2/2 = 2x  e^x +c 3y+y^2= 2xe^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 2e^x/3+2y=0 2e^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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dy/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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0maybe this will clear it up some
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