Question

Find the general solution to these differential equations. xy+y'=5x

Answer 1

@agent0smith

Answer 2

answer was y=5+Ce^(-x^2/2)

Answer 3

woudln't it be \[-Ce^\frac{ x^2 }{ 2 } + 5\]

Answer 4

@agent0smith

Answer 5

"wouldn't it be.."

No it wouldn't. Did we make a small error near the end somewhere? Your answer looks awfully close to the book answer.

Answer 6

Need to see some steps? :o

Answer 7

i got \[y=5+Ce^{-\tfrac{1}{2}x^2}\]

Answer 8

Integrating factors? Starting with...
\[\huge \frac{dy}{dx}+xy=5x\]

Answer 9

Integrating factor is
\[\large \int x dx=\frac12x^2\]So multiply
\[\huge e^{\frac{x^2}{2}}\]to the entire expression...
\[\huge e^{\frac{x^2}{2}}\frac{dy}{dx}+ e^{\frac{x^2}{2}}xy=5x e^{\frac{x^2}{2}}\]

Answer 10

Turns out the left-hand side is just
\[\huge \frac{d}{dx}\left(y e^{\frac{x^2}{2}}\right)=5x e^{\frac{x^2}{2}}\]