Differential Equations

Topic overview

For differential equation questions, first distinguish whether it is separable or in linear form, then deal with the initial value, domain and long-term behaviour. The really tricky part is often partial fraction decomposition.

Key concepts

If $dy/dx=f(x)g(y)$ , then $dy/g(y)=f(x)dx$ . After integrating, substitute the initial value to find the constant. When encountering a structure such as $y/(y+a)$ , first rewrite it or apply partial fractions.

Key points

◆Do not lose the balanced solution when separating cases
◆Keep the constant of integration before substituting the initial value
◆Check the logarithm's argument and the model's range

Worked examples

Try each example yourself before checking the explanation.

1Separate after partial fractions

Solve $dy/dx=x(y+1)/y$ .

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