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求解一介常微分方程 dydt=ay\frac{dy}{dt}=aydtdy=ay
syms y(t) a; eqn = diff(y, t) == a*y; S = dsolve(eqn)
增加条件,初值 y(0)=5y(0) = 5y(0)=5
syms y(t) a; eqn = diff(y, t) == a*y; cond = y(0) = 5; S = dsolve(eqn, cond)
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求解二阶常微分方程 d2ydu2=ay\frac{d^2y}{du^2}=aydu2d2y=ay
syms y(t) a; eqn = diff(y, t, 2) == a*y; S = dsolve(eqn)
增加条件, y(0)=b,y′(0)=1y(0) = b, y'(0) = 1y(0)=b,y′(0)=1
syms y(t) a b; eqn = diff(y, t, 2) == a*y; Dy = diff(y, t); cond = [y(0) == b, Dy(0) == 1]; S = dsolve(eqn, cond)
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求解常微分方程组
dydt=zdzdt=−y \frac{dy}{dt}=z\\ \frac{dz}{dt}=-y dtdy=zdtdz=−ysyms y(t) z(t) eqns = [diff(y, t) == z, diff(z, t) == -y]; s = dsolve(eqns)