Latihan 4.docx

> ###latihan 4 > ##no 1 > pd:=diff(y(x),x)=(x+3)/(2*y(x) + 1) ; d x3 pd := y( x ) dx 2 y( x )1 > dsolve(pd,y(x),implicit); x2 3 xy( x ) 2y( x )_C10 2 > restart;## no 2 > pd:=(x^3 -2*x+1)

+

diff(y(x),x)*(y(x)^3+3*y(x)^2+2); d pd := x 32 x1 y( x )  ( y( x ) 33 y( x ) 22 )  dx 

> > dsolve(pd,y(x)); x

x4 1 x 2 y( x ) 4y( x ) 32 y( x )_C10 4 4

> restart; ##no 3 > pd:= diff(y(x),x)-3*y(x)-5*exp(2*x); d (2 x) pd :=  y( x ) 3 y( x )5 e  dx  > #faktor integrasi > mu:=intfactor(pd); d (2 x)   := intfactor   y( x ) 3 y( x )5 e    dx  

> #penyelesaian > dsolve(pd,y(x)); y( x )( 5 e

( x )

_C1 ) e

(3 x)

> restart;#no 4 > pd:=diff(y(x),x)+2*y(x)/x=3*x+1; d 2 y( x ) pd :=  y( x )  3 x1 x  dx  > #faktor integrasi > mu:=intfactor(pd); d 2 y( x )  := intfactor   y( x )  3 x1  d x x   

> #penyelesaian > dsolve(pd,y(x));

y( x )

3 x 2 x _C1   2 4 3 x

> restart;#no 5 > pd:= diff(y(x),x$2)-3*diff(y(x),x)-4*y(x)=6*exp(3*x); 2 d (3 x) d  pd :=  2 y( x ) 3  y( x ) 4 y( x )6 e  dx   dx  > dsolve(pd,y(x)); y( x )e

( x )

_C2e

(4 x)

3 (3 x) _C1 e 2

> restart;#no6 > pd:=diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=3*exp(x); 2 d d  pd :=  2 y( x ) 3  y( x ) 2 y( x )3 e x  dx   dx  > dsolve({pd,y(0)=1,D(y)(0)=2},y(x)); y( x )( 3 x4 e x3 ) e x > restart;#no7 > pd:=diff(y(x),x)=(2 *y(x)+3)/(2*x - 1); pd :=

d 2 y3 y( x ) dx 2 x1

> dsolve(pd,y(x)); Error, (in ODEtools/info) y(x) and y cannot both appear in the given ODE.

>