求简单微分方程

求解一介常微分方程 $\frac{dy}{dt}=ay$

syms y(t) a;
eqn = diff(y, t) == a*y;
S = dsolve(eqn)
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增加条件，初值 $y(0)=5$

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 $\frac{d^{2}y}{d{u}^2}=ay$

syms y(t) a;
eqn = diff(y, t, 2) == a*y;
S = dsolve(eqn)
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增加条件， $y(0)=b,y^{\prime }(0)=1$

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
$$\begin{gathered} \frac{dy}{dt}=z \\ \frac{dz}{dt}=-y \end{gathered}$$

syms y(t) z(t)
eqns = [diff(y, t) == z, diff(z, t) == -y];
s = dsolve(eqns)
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