Topic explanation

Standard explanation

Write all y terms with dy and x terms with dx, integrate both sides, then solve if required.

Key points

• Separable equations
• rule
• worked example
• Separable equations: Write all y terms with dy and x terms with dx, integrate both sides, then solve if required.
• CONCEPT AND RULE: Write all y terms with dy and x terms with dx, integrate both sides, then solve if required.
• METHOD: For separable equations, identify the given information and required result. Select the matching def
• Write all y terms with dy and x terms with dx, integrate both sides, then solve if required.
• Worked pattern: dy/dx=xy gives dy/y=x dx, so ln|y|=x^frac22+C.

Labelled diagram