How do you solve for xy'−y=3xy given y(1)=0?

overrated3245w 2022-09-29 Answered
How do you solve for xy'−y=3xy given y(1)=0?
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Answers (1)

Matteo Estes
Answered 2022-09-30 Author has 9 answers
x d y d x = 3 x y + y
x d y d x = y ( 3 x + 1 )
d y y = 3 x + 1 x d x
Integrating;
d y y = 3 x + 1 x d x
d y y = ( 3 + 1 x ) d x
ln ( y ) = 3 x + ln ( x ) + c
y = e 3 x + ln ( x ) + c
And finally;
y = e 3 x × e ln ( x ) × e c = A x e 3 x
where A = e c
We can now find the value of the constant A;
0 = A e 3
A=0
The particular solution to your equation is then:
y = 0 x e 3 x = 0
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