NCERT Mathematics, Class 12, textbook pages 300–337 (Part II)

How to help your child with Class 12 Maths Chapter 9, Differential Equations, at home

Order, degree and solving first-order equations, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

dP/dt = kP → P = P₀eᵏᵗ

NCERT Class 12 Maths Chapter 9 Differential Equations: what it teaches

Your teen forms differential equations, finds order and degree, and solves first-order equations by separating variables, homogeneous methods and linear equations with integrating factors.

Why it matters later. Differential equations model physics, biology, economics and engineering.

See it: this chapter in pictures

(y″)³ + y′ = 0order 2 (highest derivative)degree 3 (its power)
Order first, then degree.
dy/dx = ydy/y = dx → ln y = x + Cy = Ceˣ
Separate, then integrate.
dy/dx + y = eˣIF = eˣy = eˣ/2 + Ce⁻ˣ
Linear equations use an integrating factor.

You need

  • a formula sheet
  • growth and cooling examples

Tonight’s 60 minutes

  1. Find order and degree of (d²y/dx²)³ + dy/dx = 0 (2, 3).
  2. Solve dy/dx = y (y = Ceˣ).
  3. Model population growth dP/dt = kP.
  4. Solve dy/dx + y = eˣ with an integrating factor.

Words to use

  • differential equation
  • order
  • degree
  • separable
  • homogeneous
  • integrating factor

Watch for

  • Degree when derivatives appear inside other functions. Degree is defined only for polynomial equations in derivatives.
  • Losing the constant when separating. Add one constant after integrating.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

Youdy/dx = y?

Your childSeparate: ln y = x + C, so y = Ceˣ.

A game for this week: Model it

  1. Pick a growth or cooling situation.
  2. Write the differential equation.
  3. Solve it.
  4. Predict a value.

A 5-day plan, 60 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Population growth.
  • Cooling of tea.
  • Radioactive decay.
  • Loan interest.

Quick check

Ask these at the end of the week. Tap to see the answer.

Order and degree of (y″)³ + y′ = 0?

2 and 3.

General solution of dy/dx = y?

y = Ceˣ.

Integrating factor of dy/dx + y = eˣ?

eˣ.

Ready for the next chapter when your child…

  • Finds order and degree.
  • Solves separable and linear equations.
  • Models real situations.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

What is a differential equation?

An equation involving derivatives of a function.

What is an integrating factor?

A multiplier that makes a linear equation easy to integrate.

Where are they used?

Population, cooling, circuits and motion.