Differential equations

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equation, then multiply the guess by xk, where kis the smallest positive integer such that no term in xkyp( x) is a solution of the homogeneous problem. Reduction of Order Homogeneous Case Given y 1( x) satis es L[ y] = 0; nd second linearly independent solution as v( x) = v( x) y 1( x) : z= v0satis es a separable ODE. Nonhomogeneous Case Given y. will use the product/ quotient rule and derivatives of y will use the chain rule.

`cheat sheet for differential calculus equations`

The “ trick” is to The “ trick” is to differentiate as normal and every time you differentiate a y you tack on a y ′ ( from the chain rule). Write down equation relating quantities and differentiate with respect to t using implicit differentiation ( i.