Differential Equation and Applications — Flashcards
Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce
20 flashcards for Differential Equation and Applications (Maharashtra Board Class 12 Mathematics & Statistics -Commerce) to test yourself on key terms.
Interactive on Super Tutor
Studying Differential Equation and Applications? 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.
What is a differential equation? Provide the definition and give two examples.
Answer
A differential equation is an equation involving dependent variable(s), independent variable(s), and derivatives of the dependent variable(s) with respect to the independent variable. Examples: 1) dy…
How do you determine the ORDER of a differential equation? Give examples with different orders.
Answer
The ORDER is the highest order derivative present in the equation. Examples: • dy/dx = y + x → Order = 1 (highest derivative is first order) • d²y/dx² + 3(dy/dx) - 2y = 0 → Order = 2 (highest derivat…
How do you find the DEGREE of a differential equation? Solve this step-by-step: Find the degree of (d²y/dx²)³ = 2 + (dy/dx)²
Answer
Step-by-step method: 1) Make all derivatives free from fractional/negative indices 2) Identify the highest order derivative 3) Find its power For (d²y/dx²)³ = 2 + (dy/dx)²: • Already free from fracti…
What is the difference between General Solution and Particular Solution of a differential equation?
Answer
GENERAL SOLUTION: • Contains arbitrary constants • Number of constants = order of equation • Example: y = Ae^x + Be^(-x) (2 constants for 2nd order) PARTICULAR SOLUTION: • Obtained by giving specific…
Solve this step-by-step using variable separation: dy/dx = (1+y)/(1+x)
Answer
Step 1: Separate variables dy/(1+y) = dx/(1+x) Step 2: Integrate both sides ∫dy/(1+y) = ∫dx/(1+x) Step 3: Apply integration log(1+y) = log(1+x) + log c log(1+y) = log[c(1+x)] Step 4: Remove logarit…
When do we use substitution in differential equations? Solve: (2x - 2y + 3)dx - (x - y + 1)dy = 0
Answer
Use substitution when variables cannot be separated directly. Step 1: Rearrange dy/dx = (2x - 2y + 3)/(x - y + 1) = (2(x-y) + 3)/(x-y+1) Step 2: Substitute x - y = t dt/dx = 1 - dy/dx, so dy/dx = 1 …
What is a Homogeneous Differential Equation? How do you identify one?
Answer
DEFINITION: A differential equation f(x,y)dx + g(x,y)dy = 0 is homogeneous if f(x,y) and g(x,y) are homogeneous functions of the same degree. IDENTIFICATION TEST: Replace x with λx and y with λy in b…
Solve this homogeneous equation step-by-step: (x² + y²)dx - 2xy dy = 0
Answer
Step 1: Verify it's homogeneous Both x² + y² and 2xy have degree 2 ✓ Step 2: Rearrange dy/dx = (x² + y²)/(2xy) Step 3: Substitute y = tx, dy/dx = t + x(dt/dx) t + x(dt/dx) = (x² + t²x²)/(2x·tx) = (1…
+12 more flashcards
Practise AllFrequently Asked Questions
What are the important topics in Differential Equation and Applications for Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
How many flashcards are available for Differential Equation and Applications?
How should I revise Differential Equation and Applications for the Maharashtra 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 Equation and Applications
For serious students
Get the full Differential Equation and Applications chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Maharashtra Board Class 12 Mathematics & Statistics -Commerce. Free to start, no card needed.