Differential Equations — Class 12 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Differential Equations" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Differential Equations" — 8 important questions with detailed answers for CBSE boa…
By Syllab.in · Updated
Key Questions Covered:
- Solve the differential equation dy/dx = 2x with the initial condition y(0) = 1.
- Solve the differential equation dy/dx + 2y = e^(-2x).
- Solve the differential equation (x + y) dx = (x + y + 1) dy.
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Solve the differential equation dy/dx = 2x with the initi… | ✓ Solved |
| Solve the differential equation dy/dx + 2y = e^(-2x). | ✓ Solved |
| Solve the differential equation (x + y) dx = (x + y + 1) dy. | ✓ Solved |
Showing 3 of 8 questions
Q1: Solve the differential equation dy/dx = 2x with the initial condition y(0) = 1.
To solve dy/dx = 2x with y(0) = 1:
Step 1: Separate variables (already separated).
dy = 2x dx
Step 2: Integrate both sides.
∫ dy = ∫ 2x dx
y = x² + C
Step 3: Apply initial condition y(0) = 1.
1 = 0² + C
C = 1
Step 4: Write the particular solution.
y = x² + 1
Final Answer: y = x² + 1
Q2: Solve the differential equation dy/dx + 2y = e^(-2x).
To solve linear DE: dy/dx + 2y = e^(-2x):
Step 1: Identify the form.
This is dy/dx + P(x)y = Q(x)
where P(x) = 2 and Q(x) = e^(-2x)
Step 2: Find integrating factor.
I.F. = e^(∫ P(x) dx)
= e^(∫ 2 dx)
= e^(2x)
Step 3: Multiply the equation by I.F.
e^(2x) × dy/dx + 2e^(2x) × y = e^(2x) × e^(-2x)
e^(...
Q3: Solve the differential equation (x + y) dx = (x + y + 1) dy.
To solve (x + y) dx = (x + y + 1) dy:
Step 1: Rearrange the equation.
(x + y) dx - (x + y + 1) dy = 0
Step 2: Use substitution.
Let u = x + y, then du = dx + dy
So dx = du - dy
Step 3: Substitute in the equation.
u(du - dy) - (u + 1) dy = 0
u du - u dy - u dy - dy = 0
u du - 2u dy - dy = 0
u du =...
Showing 3 of 8 questions. Visit the full page for complete solutions.