Write the equation in the form y′=f(y/x) then use the substitution y=xu to find an implicit general solution. Then solve the initial value problem.

y′=5y2+4x2xy, y(1)=3

The resulting differential equation in x x and u u can be written as xu′= which is separable.

Separating variables we arrive at du=dx/x

Separating variables and and simplifying the solution can be written in the form u2+1=Cf(x) where C is an arbitrary constant and f(x)= .

Transforming back into the variables x and y and using the initial condition to find C we find the explicit solution of the initial value problem is y = .

Looks like the ODE is supposed to be

In that case, let , so that . Substitute these into the ODE to get

which is separable as

Integrate both sides to get

We can solve for :

Replace to get the general solution,

Given that , we find

so the particular solution is

answer: it is 1: 47 pm

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".