Maple 2021中的常微分方程Student[ODEs]学习包，自动显示微分方程的分步求解过程细节

Maple 2021新增加了Student[ODEs]微分方程学生包，该学生包可以自动显示计算步骤和详细结果，与以前版本中的微积分、线性代数、数值分析、优化学生包一起辅助老师教学和学生自学。

Student[ODEs]

命令：ODESteps

功能：显示ode、ivp或odes的分步求解过程

• 一阶常微分方程

• 一阶IVPs常微分方程初值问题

• 二阶常微分方程

• 二阶IVPs常微分方程初值问题

• Cauchy-Euler 方程

• 级数解

• 特殊函数解

• 常微分方程系统

Diff(u(x), x) = c*u(x) + x^2

restart;

with(Student[ODEs]);

ode1 := Diff(u(x), x) = c*u(x) + x^2;

ODESteps(ode1);   #显示计算细节

with(Student:-ODEs);

ode2 := diff(y(x), x) - y(x) - x*exp(x) = 0;

ODESteps(ode2);

restart

with(Student:-ODEs);

ivp1 := {t^2*(z(t) + 1) + z(t)^2*(t - 1)*diff(z(t), t) = 0, z(3) = 1};

ODESteps(ivp1);

restart;

with(Student:-ODEs);

ode4 := 2*x*diff(y(x), x) - 9*x^2 + (2*diff(y(x), x) + x^2 + 1)*diff(y(x), x, x) = 0

ODESteps(ode4)

with(Student:-ODEs);

ivp5 := {diff(y(x), x, x) - diff(y(x), x) - x*exp(x) = 0, eval(diff(y(x), x), x = 0) = 0, y(0) = 1};

ODESteps(ivp5)  #显示计算细节

with(Student:-ODEs);

ode6 := x^2*diff(y(x), x, x) - 4*x*diff(y(x), x) + 2*y(x) = 0;

ODESteps(ode6)

restart;

ode7 := x^2*diff(y(x), x, x) + x*diff(y(x), x) + 5*x*y(x) = 0

Student:-ODEs:-ODESteps(ode7)

restart

with(Student:-ODEs);

ode8 := x^2*diff(y(x), x, x) + 4*x*diff(y(x), x) + (25*x^2 - 9)*y(x) = 0;

ODESteps(ode8)

restart

with(Student:-ODEs);

high_order_ode1 := diff(y(x), x, x, x) + 3*diff(y(x), x, x) + 4*diff(y(x), x) + 2*y(x) = 0;

ODESteps(high_order_ode1)

restart;

with(Student:-ODEs);

high_order_ivp1 := {diff(y(x), x, x, x) + 3*diff(y(x), x, x) + 4*diff(y(x), x) + 2*y(x) = 0, eval(diff(y(x), x), x = 0) = -1, eval(diff(y(x), x, x), x = 0) = 2, y(0) = 1};

ODESteps(high_order_ivp1)