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MATH 2574H
Jasmine Foo

Overall TipsDont forget constant right after integratingRearrange all equations to look like whatever form you are trying to solveDont forget to try partial fractions if an integral doesnt seem solvableYou dont necessarily have to solve for y explicitly as long as youve integrated and have some sort of a solution but solve for y when feasibleWhen finding an integrating factor to make an equation look exact dont just look at the functions M and N to determine beforehand that you cant get a function of y or just xThere may be multiple ways to solve the problem so try to find the easiest way to save time and make less mistakesWrite down the different techniques in order of master list and then cross them off y sep lin ber hom exact exact subFirst Order Linear ODEdyPxyQxForm dxSolutionPxdxo1 Calculate integrating factor xeo2 Multiply original equation by xdyPxdxPxdxPxdxeePxyQxedxdPxdxyeYou know the left side of the equation is equal todxbecause by differentiating this by the product rule you get back the left side of the equationdPxdxPxdxyeQxedxPxdxPxdxo3 Integrate yeQxedxCo4 Solve for ySeparable EquationsdyMxNyForm dxSolutiono1 Rewrite equation so that all x terms are one 1 side and all y terms are on NydyMxdxanother side o2 Integrate each side with respect to whatever variable is on that side also combine the integration constants into a single oneNydyMxdxCo3 Simplify and solve for y if needed
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