Differential Equations

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Calculus - Geometry

snashuhaimdinx Created by 6 mon ago

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v=y/x, dy/dx = dv/dx(x) + v

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y = c1*exp(r1x) * c2*exp(r2x)

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y = c1*exp(r*x) + c2*exp(r*x)

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y = exp(ax) * (c1*cos(Bx) + c2*sin(Bx)) where a is before +-, and B is coefficient on i

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y2 = y1*INT((exp(-INT(P(t)dt)/(y1^2))dt

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My = Nx

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compare INTMdx and INTNdy. count all unique terms and all alike terms once, set equal to C and solve.

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rho(t) = exp(INTP(t)dt)

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get coefficient on y = 1. then: y(t) = (1/rho(t)) * INT(rho(t)*Q(t))dt

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dQ/dt + ro/v(t) *Q =ri*ci

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Q = mass of solute in water ro = rate out of tank ri = rate into tank ci = concentration entering v(t) = volume of liquid as fxn of time = V0 + (ri-ro)t

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Divide the coefficient on the highest order variable ST the coefficient on said variable is 1.

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y1 = y0 + h*f(x0, y0) where y1 = the answer after one step y0 = initial condition (given) h = integrating factor (given) f(x0, y0) = the RHS of given function solved at the initial condition

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