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10 questions from this quiz
One or more arbitrary constants
dydx\frac{dy}{dx}dxdy
dydx=g(x)h(y)\frac{dy}{dx} = g(x) h(y)dxdy=g(x)h(y)
A constant of integration CCC
Separate variables: 1ydy=xdx\frac{1}{y} dy = x dxy1dy=xdx
y=C1ex22y = C_1 e^{\frac{x^2}{2}}y=C1e2x2
Solving the characteristic equation
m2−3m+2=0m^2 - 3m + 2 = 0m2−3m+2=0
y(x)=C1em1x+C2em2xy(x) = C_1 e^{m_1 x} + C_2 e^{m_2 x}y(x)=C1em1x+C2em2x
y(x)=C1ex+C2e2xy(x) = C_1 e^{x} + C_2 e^{2x}y(x)=C1ex+C2e2x
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