Page 1 of 1

Lett difflikning

Posted: 20/10-2009 07:44
by sveioen
[tex]2y`+y=e^x[/tex]
[tex]y`+\frac{1}{2}y=\frac{1}{2}e^x[/tex]
[tex]e^{\frac{1}{2}x} y =\frac{2}{3}e^{\frac{3}{2}x}+C[/tex]
[tex]y =\frac{2}{3}e^{\frac{3}{2}x}\times e^{-\frac{1}{2}x}+C[/tex]
[tex]y(x)= \frac{2}{3}e^x +e^{-\frac{x}{2}}C[/tex]

Fasit sier derimot
[tex]y(x)= \frac{1}{3}e^x +e^{-\frac{x}{2}}C[/tex]

Hvem har rett?

Posted: 20/10-2009 08:50
by Betelgeuse
Fasiten har nok rett :p

[tex](e^{\frac{1}{2}x}y)\prime = \frac{1}{2}e^{\frac{3}{2}x} \Rightarrow e^{\frac{1}{2}x}y = \frac{1}{2} \int e^{\frac{3}{2}x}dx = \frac{1}{2}\frac{2}{3} e^{\frac{3}{2}x} + C \Rightarrow y = \frac{1}{3}e^x + Ce^{-\frac{1}{2}x}[/tex]

Posted: 20/10-2009 09:22
by sveioen
Det er det dummeste, glemte å ta med [tex]\frac{1}{2}[/tex]. Takker.