Question

Determine whether the function y=x^2 is a solution of the differential equation 2xy' + 4y=10x^3

Answer 1

can i say yes it is ?

Answer 2

yes is the answer, but how did you get it? o.o

Answer 3

im still learning but

if you differentiate the problem

Answer 4

you end up with

2y'+4=10x^2

6 =10 x^2

6/10 = x^2

3/5= x^2

i dunno is that how you get the answer ?

Answer 5

to be honest i'm not really sure what you did XD but I think i have to do something with integrals

Answer 6

i used the power rule :P
or tried

Answer 7

then i used my logic super wacked (logic) and got the answer

Answer 8

then i will probably be missing somthing of course

Answer 9

y=x^2
y'=2x
multiply 2x
2xy'=4x^2
y=x^2
2xy'=4y=4x^2
2xy'+4y=2*4x^2
so 2xy'+4y=8x^2
so it is not the solution of the differential equation

Answer 10

2xy' + 4y=10x^3

y= x^2
y'= 2x

Plug in those values:
2x(2x) + 4(x^2)= 10x^3

Solve:
4x^2 + 4x^2= 10x^3
LHS DOES NOT = RHS THEREFORE NOT A SOLUTION