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Method of Characteristics - Lagrange-Charpit Equations

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Wave equation with piecewise-defined Cauchy data

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Cauchy problem of a 1st order ODE, given 2 solutions?

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$k$ such that interval of solution of a Cauchy problem contains 0 and it is the biggest possible

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#ordinary-differential-equations #cauchy-problem
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Cauchy-Lipschitz Theorem for second order ODEs

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Population growth problem, when its' growth is 3x increased at the time $t=1$.

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71
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Population growth - population grows proportionally, increasing 2x from $t=0$ and $t=1$ and reaching 10000 at $t=2$

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#ordinary-differential-equations #cauchy-problem
59
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Cauchy problem, $x' -\frac{x}{t}=t, x(1)=0$

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#ordinary-differential-equations #cauchy-problem
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How to solve this Cauchy's problem?

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304
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Proving the solution of a Cauchy problem is continuous

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Nonlinear PDE of form $u_y=F(u_x)$

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#partial-differential-equations #nonlinear-system #characteristics #hyperbolic-equations #cauchy-problem
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Differentiability of P.D.E With given initial conditions on Its Characteristic base curve.

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Characteristic equations of Cauchy Problem.

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Critical points in Cauchy problem

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Cauchy problem: $x'-cot(t)\cdot x =2tsint; x\left(\frac{\pi}{2}\right)=\frac{\pi^2}{4}$

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