- #1
Char. Limit
Gold Member
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My AP Calculus class touched on differential equations recently, only for a moment. I immediately noticed that most differential equations that involved only multiplication were easy. However, I was soon stumped by some addition differential equations. How do you solve these undoubtedly bonehead simple equations?
(Note: As the work is being done independently, it isn't homework, and as such I'm not sure if I need to show what I've done so far. Besides, I don't know much at all about differential equations. I'd have nothing to show.)
[tex]\frac{dy}{dx}=x+y[/tex]
[tex]\frac{dy}{dx}=x-y[/tex]
[tex]\frac{dy}{dx}=y-x[/tex]
And generalizations...
[tex]\frac{dy}{dx}=ax+by[/tex]
[tex]\frac{dy}{dx}=ax-by[/tex]
[tex]\frac{dy}{dx}=ay-bx[/tex]
for constant real a and b.
(Note: As the work is being done independently, it isn't homework, and as such I'm not sure if I need to show what I've done so far. Besides, I don't know much at all about differential equations. I'd have nothing to show.)
[tex]\frac{dy}{dx}=x+y[/tex]
[tex]\frac{dy}{dx}=x-y[/tex]
[tex]\frac{dy}{dx}=y-x[/tex]
And generalizations...
[tex]\frac{dy}{dx}=ax+by[/tex]
[tex]\frac{dy}{dx}=ax-by[/tex]
[tex]\frac{dy}{dx}=ay-bx[/tex]
for constant real a and b.