Example 1 · level 1
Find the order of the differential equation (y‴)³ + y² + 4(y″)³ = x².
- 3
- 2
- 1
- Not defined
Show solution
- The highest derivative is y‴, of order 3.
- So the order is 3.
Answer: 3
CLASS 12 MATHS · DIFFERENTIAL EQUATIONS
Differential equations: order, degree and solutions
Order = highest derivative present. Degree = power of that highest derivative once the equation is a polynomial in derivatives (not defined if a derivative sits inside sin, eˣ, etc.). Separate variables to solve dy/dx = ky.
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Worked examples
Example 2 · level 2
Find the degree of the differential equation (dy/dx)³ + 3y = x².
- 4
- Not defined
- 3
- 1
Show solution
- The highest derivative is dy/dx, and it is raised to the power 3.
- So the degree is 3.
Answer: 3
Example 3 · level 3
Solve dy/dx = y with y(0) = 4, and find y when x = ln 2.
Show solution
- y = 4e^(x).
- At x = ln 2: y = 4e^( ln 2) = 4 × 2 = 8.
Answer: 8