Class 12 Math: Differential Equations Solved Examples & Step Solutions
NexPro Tools Mathematics TeamJune 5, 20266 min read
The best way to gain confidence in mathematics is by studying solved examples. By analyzing how formulas are applied step-by-step, you learn how to tackle complex questions in your homework and exams. Let's walk through standard worked examples for Class 12 Differential Equations.
Step-by-Step Solved Problems
Example 1: Separable Differential Equation
Question: Solve differential equation: dy/dx = (1 + y²) / (1 + x²).
Worked Solution Steps:
- Separate variables: dy / (1 + y²) = dx / (1 + x²).
- Integrate both sides: ∫ dy / (1 + y²) = ∫ dx / (1 + x²).
- Result: tan⁻¹(y) = tan⁻¹(x) + C.
Final Answer: \tan^{-1}(y) = \tan^{-1}(x) + C
Self-Practice Method
When studying these examples, cover the solution with a sheet of paper and attempt to solve the question on your own. If you get stuck, reveal the steps one by one to identify where your logic deviated. This active recall method builds long-term problem-solving skills.
📚 Class 12 Math Resource Hub for Differential Equations:
• 🧮 Interactive Solver: Solve Differential Equations Problems - Verify steps in real-time.
• 📝 Timed Practice Quiz: Take Differential Equations Online Quiz - Test your speed and concepts.
• 📄 Printable Worksheet: Download Differential Equations PDF Worksheet - Interactive problems with answers.
• 📐 Formula Sheet: View Differential Equations Key Equations - Complete revision references.
• 🔄 Next Topic Guide: Vector Algebra Study Notes
• 🎓 Syllabus Overview: Class 12 Mathematics Portal - Access all chapter guides.