$u(t)=e^{At} u_0$ is solution of the IVP $u'(t)=Au(t)$ and $u(0)=u_{0}$.
65077
Differential Equations, unique solution
57811
Properties of the solution of the Ordinary Differential Equation $y' = y(y-1)(y-2)$ as per the Initial conditions?
72872
Number of zeroes of solution to $y''(x)+e^{x^2}y(x)=0$ in $[0,3π]$
127329
A problem about wave equation
53610
What is the difference between $Q=\Delta U+W$ and $\Delta U=Q+W$?
152293
Solution of $y''+xy=0$
122166
Significance of $i$ in the Schrödinger equation
48686
Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
75452
Initial value problem with $t$ and $x'$
38839
Exponential of the differential operator
14576
$(U\cap W)^0 = U^0 + W^0$
62816
Proof that ODE solutions with Wronskian identically zero are linearly dependent
117387
Can we safely assume $\Psi(x,t) = \psi(x)e^{-i\omega t}$ always in QM?
116427
$(c^{\mu}\partial_{\mu}-m)\phi(x)=0$ not Lorentz-invariant?
121547
Differential equation for Harmonic Motion
101166
Show that for $\eta > 0$, $\alpha_\eta=-\infty$ and for the Cauchy problem $z'=x-z^2,z(0)=\eta$ the saturated solution is defined up to $+\infty$.