Student[ODEs][Solve]
ByLaplaceTransform
Solve a linear ODE using the Laplace transform
Calling Sequence
Parameters
Description
Examples
Compatibility
ByLaplaceTransform(ODE, IC, y(x))
ODE
-
a linear ordinary differential equation
IC
set; a set of two initial conditions
y
name; the dependent variable
x
name; the independent variable
The ByLaplaceTransform(ODE, IC, y(x)) command finds the solution of a linear ordinary differential equation ODE with initial conditions IC by using the Laplace transform.
withStudentODEsSolve:
ode1≔diffxt,t,t+2diffxt,t+2xt=0
ode1≔ⅆ2ⅆt2xt+2ⅆⅆtxt+2xt=0
ic1≔evaldiffxt,t,t=0=−2,x0=1
ic1≔ⅆⅆtxtt=0|ⅆⅆtxtt=0=−2,x0=1
ByLaplaceTransformode1,ic1,xt
xt=ⅇ−tcost−ⅇ−tsint
ode2≔diffxt,t,t+diffxt,t−6xt=sint
ode2≔ⅆ2ⅆt2xt+ⅆⅆtxt−6xt=sint
ic2≔evaldiffxt,t,t=0=2,x0=−3
ic2≔ⅆⅆtxtt=0|ⅆⅆtxtt=0=2,x0=−3
ByLaplaceTransformode1,ic2,xt
xt=−3ⅇ−tcost−ⅇ−tsint
ode3≔diffxt,t,t+4diffxt,t+4xt=exp2t
ode3≔ⅆ2ⅆt2xt+4ⅆⅆtxt+4xt=ⅇ2t
ic3≔evaldiffxt,t,t=0=−2,x0=1
ic3≔ⅆⅆtxtt=0|ⅆⅆtxtt=0=−2,x0=1
ByLaplaceTransformode1,ic3,xt
ode4≔diffxt,t,t−6diffxt,t+13xt=t
ode4≔ⅆ2ⅆt2xt−6ⅆⅆtxt+13xt=t
ic4≔evaldiffxt,t,t=0=−2,x0=1
ic4≔ⅆⅆtxtt=0|ⅆⅆtxtt=0=−2,x0=1
ByLaplaceTransformode1,ic4,xt
ode5≔diffxt,t,t+4diffxt,t+4xt=exp−2t
ode5≔ⅆ2ⅆt2xt+4ⅆⅆtxt+4xt=ⅇ−2t
ic5≔evaldiffxt,t,t=0=−2,x0=2
ic5≔ⅆⅆtxtt=0|ⅆⅆtxtt=0=−2,x0=2
ByLaplaceTransformode1,ic5,xt
xt=2ⅇ−tcost
The Student[ODEs][Solve][ByLaplaceTransform] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
See Also
dsolve
inttrans[laplace]
Student
Student[ODEs]
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