Mathematics, 25.02.2020 18:04, badpotterchris
(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: 2
Mathematics, 21.06.2019 14:50, tinasidell1972
Need to increase the numbers of customers i talk to daily by 20% how many customers do i need to talk to if i talk to a average of 8 customers per hour during an 8 hour shift
Answers: 2
Mathematics, 21.06.2019 21:00, angelaguero536
In the field of thermodynamics, rankine is the unit used to measure temperature. one can convert temperature from celsius into rankine using the formula , what is the temperature in celsius corresponding to r degrees rankine? a. 9/5(c - 273) b. 9/5(c + 273) c. 5/9( c - 273) d. 5/9( c + 273)
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...
English, 26.02.2021 18:30
English, 26.02.2021 18:30
Mathematics, 26.02.2021 18:30
Mathematics, 26.02.2021 18:30
English, 26.02.2021 18:30