cocomelon

19.03.2020 • 

Mathematics

(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.

Ответ:

godchaux15395

15.01.2022

Mathematics

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614 because if you take the number of students and divide that by the medita session is you get 20.46666 and on and then you multiply that by 30 minute long is that his car and you get the number you started with.

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