RD Sharma Solutions for Class 12 Maths Chapter 22 Differential Equations – PDF Download

RD Sharma Solutions for Class 12 Maths Chapter 22 – Differential Equations provide a clear and simplified approach to understanding various forms of differential equations and their real-world applications. From concepts like Newton’s Law of Cooling to growth and decay models and problems in coordinate geometry, these RD Sharma solutions help students grasp complex ideas in an easy-to-follow format.

Each solution is presented in a step-by-step manner, using simple language to ensure that students at all levels can understand and apply the methods effectively. These solutions serve as a valuable resource for tackling high-difficulty questions, especially in competitive exams like JEE Main and JEE Advanced.

Designed in accordance with the latest CBSE syllabus and marking scheme, the RD Sharma Class 12 Differential Equations solutions not only support exam readiness but also strengthen a student’s overall conceptual foundation. Using these detailed, exercise-wise solutions can significantly boost confidence and scoring potential.

Download RD Sharma Solutions for Class 12 Maths Chapter 22 Differential Equations PDF

RD Sharma Class 12 Maths Solutions Chapter 22 Differential Equations cover all the questions from the textbook, crafted by expert Mathematics teachers at Infinity Learn. Download our free PDF of Chapter 22 Differential Equations RD Sharma Solutions for Class 12 to boost your performance in board exams and competitive exams.

Access answers to RD Sharma Solutions For Class 12 Chapter 22 Differential Equations

Question: Determine the order and degree of the differential equation:

(d³x/dt³) + (d²x/dt²) + (dx/dt)² = e^t

Solution:

• Order: Highest derivative is d³x/dt³ ⇒ 3
• Degree: Power of highest order derivative is 1 ⇒ 1
• Nature: Non-linear due to (dx/dt)²

Question: Form the differential equation representing the family of curves:

y² = (x - c)³

Solution:

1. Differentiate both sides: 2y dy/dx = 3(x - c)²
2. From the original equation: x - c = y^2/3
3. Substitute back to eliminate c and form the differential equation.

Question: Solve the differential equation: dy/dx + y tan x = sin x

Solution:

• Identify P(x) = tan x, Q(x) = sin x
• Integrating Factor (IF) = e^{∫tan x dx} = 1/cos x
• Multiply entire equation by IF and solve using the method of integrating factor.

Question: A balloon's surface area S is S = 4πr². If dS/dt ∝ r, find the relation between r and t.

Solution:

• Given: dS/dt = k r
• But S = 4πr² ⇒ dS/dt = 8πr (dr/dt)
• Equating: 8πr dr/dt = kr ⇒ dr/dt = k / (8π)
• Integrate: r = (k/8π)t + C