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10 cards from this deck
An equation involving an unknown function and its derivatives.
Equations involving the first derivative of a function.
The most general form, including arbitrary constants.
dydx=f(x,y)\frac{dy}{dx} = f(x, y)dxdy=f(x,y)
Equations where variables can be separated on both sides.
Integrate both sides: ∫1h(y)dy=∫g(x)dx\int \frac{1}{h(y)} dy = \int g(x) dx∫h(y)1dy=∫g(x)dx
d2ydx2+p(x)dydx+q(x)y=0\frac{d^2y}{dx^2} + p(x) \frac{dy}{dx} + q(x)y = 0dx2d2y+p(x)dxdy+q(x)y=0
Solve the characteristic equation of the differential equation.
They represent the solutions to the differential equation.
y(x)=C1em1x+C2em2xy(x) = C_1 e^{m_1 x} + C_2 e^{m_2 x}y(x)=C1em1x+C2em2x
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