Differential Equations
Madhya Pradesh Board · Class 12 · Mathematics
Flashcards for Differential Equations — Madhya Pradesh Board Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allSolve: 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,…
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