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ode_int_y

  

given the nth order linear ODE satisfied by y(x), compute the nth order linear ODE satisfied by int(y(x),x)

  

ode_y1

  

given the nth order linear ODE satisfied by y(x), compute the nth order linear ODE satisfied by diff(y(x),x)

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ode_int_y(ode, y(x))

ode_y1(ode, y(x))

Parameters

ode

-

ordinary differential equation satisfied by y(x)

y(x)

-

unknown function of one variable

Description

• 

Given a nth order linear ODE for yx, the ode_int_y and ode_y1 commands respectively compute the nth order linear ODE satisfied by ∫yxⅆx and ⅆⅆxyx.

Examples

For enhanced input output use DEtools[diff_table] and PDEtools[declare].

withDEtools,diff_table,ode_int_y,ode_y1

diff_table,ode_int_y,ode_y1

(1)

PDEtools[declare]prime=x,yx,cx

derivatives with respect toxof functions of one variable will now be displayed with '

yxwill now be displayed asy

cxwill now be displayed asc

(2)

Ydiff_tableyx:

PDEtools[declare]yx,cx,prime=x

yxwill now be displayed asy

cxwill now be displayed asc

derivatives with respect toxof functions of one variable will now be displayed with '

(3)

Now, if yx satisfies

c[0]xY[]+c[1]xYx+c[2]xYx,x+Yx,x,x,x=0

yc0+y'c1+y''c2+y''''=0

(4)

then the derivative of yx satisfies

DEtools[ode_y1]=0

y''''c0`'`y'''c0+c2y''c0`'`c2c1c0c2`'`c0y'c0c0`'`c1c02c1`'`c0yc0=0

(5)

and so, the integral of the function yx in the equation above satisfy this other ODE (the starting point)

DEtools[ode_int_y],yx=0

yc0+y'c1+y''c2+y''''=0

(6)

See Also

DEtools

 


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