Mathematics, 19.03.2020 09:35 leilaneedshelp3395
(1 point) The equation 3y′=3xy+2x2+2y2x2, (∗) can be written in the form y′=f(y/x), i. e., it is homogeneous, so we can use the substitution u=y/x to obtain a separable equation with dependent variable u=u(x).
Introducing this substitution and using the fact that y′=xu′+u we can write (∗) as y′=xu′+u=f(u) where f(u)= 1/3(3u+2u^2+2) .
Separating variables we can write the equation in the form g(u)du=dxx where g(u)= 3/(2(u^2+1)) .
An implicit general solution with dependent variable u can be written in the form ln(x)− 3/2arctan(u) =C.
Transforming u=y/x back into the variables x and y and using the initial condition y(1)=1 we find C= -(3pi)/8
Finally solve for y to obtain the explicit solution of the initial value problem y= xtan(2/3lnx+(3pi)/8) Note: You can earn partial credit on this problem.
Answers: 1
Mathematics, 21.06.2019 18:00
Jada has a monthly budget for her cell phone bill. last month she spent 120% of her budget, and the bill was 60$. what is jada’s monthly budget
Answers: 2
Mathematics, 21.06.2019 18:30
Florence price's brownies and more sells all types of cookies and pastries. on tuesdays, they markdown all brownies 75% to a sale of $1.50 a dozen. find the selling price and the markdown of a dozen brownies.
Answers: 1
Mathematics, 21.06.2019 20:00
Which of these tools or constructions is used to inscribe a hexagon inside a circle?
Answers: 1
(1 point) The equation 3y′=3xy+2x2+2y2x2, (∗) can be written in the form y′=f(y/x), i. e., it is hom...
Mathematics, 09.06.2021 04:50
Mathematics, 09.06.2021 04:50
Mathematics, 09.06.2021 04:50
Mathematics, 09.06.2021 04:50
Mathematics, 09.06.2021 04:50
Computers and Technology, 09.06.2021 04:50
Physics, 09.06.2021 04:50
Mathematics, 09.06.2021 04:50
Computers and Technology, 09.06.2021 04:50
Mathematics, 09.06.2021 04:50