Ordinary Differential Equations — Flashcards
Tamil Nadu Board · Class 12 · Mathematics
24 flashcards for Ordinary Differential Equations (Tamil Nadu Board Class 12 Mathematics) to test yourself on key terms and facts.
Interactive on Super Tutor
Studying Ordinary Differential Equations? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.
Free trial, no card needed.
An illustration from Super Tutor's Ordinary Differential Equations chapter — alongside flashcards, concept maps and practice questions.
Identify the order and degree of the differential equation: (d²y/dx²) + 5(dy/dx) + 6y = 0
Answer
Step 1: Find the highest order derivative present → d²y/dx² (second derivative) Step 2: The order is 2 Step 3: Check the power of the highest order derivative → (d²y/dx²)¹, power = 1 Step 4: The equat…
Find the order and degree of: √(1 + (dy/dx)²) = y(d³y/dx³)
Answer
Step 1: The equation contains a fractional power (square root), so it's not in polynomial form Step 2: Square both sides to eliminate the fractional power: 1 + (dy/dx)² = y²(d³y/dx³)² Step 3: Identify…
Why is degree undefined for: sin(dy/dx) + (d²y/dx²) + 3x = 0?
Answer
Answer: Because the highest order derivative (d²y/dx²) is not trapped in a transcendental function (sin, cos, exp, log), BUT the first derivative IS trapped in the sine function. Key Reason: After ide…
Classify the differential equation: (1 + x³)(dy/dx) + 6x²y = 1 + x²
Answer
Step 1: Rewrite in standard form by dividing by (1 + x³): dy/dx + [6x²/(1 + x³)]y = (1 + x²)/(1 + x³) Step 2: Check linearity criteria: - y appears only to first power ✓ - dy/dx appears only to first…
Which of these is nonlinear and why? (a) y'' + 2xy' = sin x (b) y² + y' = √x (c) y' + p(x)y = 0
Answer
Answer: (b) y² + y' = √x is nonlinear Analysis: (a) y'' + 2xy' = sin x - y'' appears to first power ✓ - y' appears to first power ✓ - No products of y and derivatives ✓ - Coefficient 2x is a function…
Form a differential equation by eliminating the constant 'a' from: y² = 4ax
Answer
Step 1: Given family of parabolas: y² = 4ax, where 'a' is arbitrary constant Step 2: Differentiate with respect to x: 2y(dy/dx) = 4a Step 3: Solve for 'a' from differentiation: a = (1/2)y(dy/dx) St…
Eliminate arbitrary constants A and B from: y = A cos x + B sin x
Answer
Step 1: Given family: y = A cos x + B sin x (contains 2 constants) Step 2: First differentiation: dy/dx = -A sin x + B cos x ... (equation 2) Step 3: Second differentiation: d²y/dx² = -A cos x - B s…
Solve using variables separable: (1 + x²)dy/dx = 1 + y²
Answer
Step 1: Recognize this is a separable equation (variables can be separated) Step 2: Rearrange to separate variables: dy/(1 + y²) = dx/(1 + x²) Step 3: Integrate both sides: ∫ dy/(1 + y²) = ∫ dx/(1 +…
+16 more flashcards
Practise AllFrequently Asked Questions
What are the important topics in Ordinary Differential Equations for Tamil Nadu Board Class 12 Mathematics?
How many flashcards are available for Ordinary Differential Equations?
How should I revise Ordinary Differential Equations for the Tamil Nadu Board Class 12 board exam?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Ordinary Differential Equations
Practice Quiz
Test yourself with a quick quiz
Important Questions
Exam-style questions with answers
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Concept Maps
See how topics connect
Syllabus
What topics to cover
For serious students
Get the full Ordinary Differential Equations chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Tamil Nadu Board Class 12 Mathematics. Free to start, no card needed.