Differential Equations — Flashcards
Madhya Pradesh Board · Class 12 · Mathematics
50 flashcards for Differential Equations (Madhya Pradesh Board Class 12 Mathematics) to test yourself on key terms and facts.
Interactive on Super Tutor
Studying 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.
Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Differential Equations.
Solve: dy/dx = e^x. Find the order and degree first.
Answer
Step 1: The highest derivative present is dy/dx, so the order is 1. Step 2: The derivative appears to the power 1, so the degree is 1. Step 3: This is already in solved form. Answer: Order = 1, Degree…
हल कीजिए: dy/dx = e^x. पहले कोटि और घात ज्ञात कीजिए।
Answer
चरण 1: उपस्थित सबसे बड़ा अवकलज dy/dx है, इसलिए कोटि 1 है। चरण 2: अवकलज घात 1 की घात में है, इसलिए घात 1 है। चरण 3: यह पहले से ही हल किए हुए रूप में है। उत्तर: कोटि = 1, घात = 1.
हल कीजिए: d^2y/dx^2 + y = 0. सामान्य हल में कितने मनमाने नियतांक होने चाहिए?
Answer
चरण 1: यह द्वितीय कोटि का अवकल समीकरण है। चरण 2: द्वितीय कोटि के समीकरण के सामान्य हल में दो मनमाने नियतांक होते हैं। चरण 3: सामान्य हल है y = a sin(x + b). उत्तर: दो मनमाने नियतांक, a और b.
Solve: d^2y/dx^2 + y = 0. How many arbitrary constants should the general solution have?
Answer
Step 1: This is a second-order differential equation. Step 2: A second-order equation has two arbitrary constants in its general solution. Step 3: The general solution is y = a sin(x + b). Answer: Two…
Find the order and degree of: (dy/dx)^2 + (dy/dx) - sin^2 y = 0.
Answer
Step 1: The highest derivative present is dy/dx, so the order is 1. Step 2: The equation is polynomial in dy/dx. Step 3: The highest power of dy/dx is 2. Answer: Order = 1, Degree = 2.
का कोटि और घात ज्ञात कीजिए: (dy/dx)^2 + (dy/dx) - sin^2 y = 0.
Answer
चरण 1: उपस्थित सबसे बड़ा अवकलज dy/dx है, इसलिए कोटि 1 है। चरण 2: समीकरण dy/dx के सापेक्ष बहुपद है। चरण 3: dy/dx की सबसे बड़ी घात 2 है। उत्तर: कोटि = 1, घात = 2.
का कोटि और घात ज्ञात कीजिए: dy/dx + sin(dy/dx) = 0.
Answer
चरण 1: उपस्थित सबसे बड़ा अवकलज dy/dx है, इसलिए कोटि 1 है। चरण 2: sin(dy/dx) के कारण समीकरण अवकलज के सापेक्ष बहुपद नहीं है। चरण 3: घात परिभाषित नहीं की जा सकती। उत्तर: कोटि = 1, घात परिभाषित नहीं।…
Find the order and degree of: dy/dx + sin(dy/dx) = 0.
Answer
Step 1: The highest derivative present is dy/dx, so the order is 1. Step 2: The equation is not polynomial in the derivative because of sin(dy/dx). Step 3: Degree cannot be defined. Answer: Order = 1,…
+42 more flashcards
Practise AllFrequently Asked Questions
What are the important topics in Differential Equations for Madhya Pradesh Board Class 12 Mathematics?
How many flashcards are available for Differential Equations?
How should I revise Differential Equations for the Madhya Pradesh 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 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
Study Plan
Step-by-step plan for this chapter
Syllabus
What topics to cover
NCERT Solutions
Every textbook question solved step by step
For serious students
Get the full Differential Equations chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Madhya Pradesh Board Class 12 Mathematics. Free to start, no card needed.