Chapter 9 : Differential Equations - Ncert Solutions for Class 12-science Maths CBSE

Your CBSE Class 12 syllabus for Maths consists of topics such as linear programming, vector quantities, determinants, etc. which lay the foundation for further education in science, engineering, management, etc. Studying differential equations will be useful for exploring subjects such as Physics, Biology, Chemistry, etc. where your knowledge can be applied for scientific investigations.

On TopperLearning, you can find study resources such as sample papers, mock tests, Class 12 Maths NCERT solutions and more. These learning materials can help you understand concepts such as differentiation of functions, direction cosines, integrals, and more. Also, you can practise the Maths problems by going through the solutions given by our experts.

Maths is considered as one of the most difficult subjects in CBSE Class 12 Science. Our Maths experts simplify complex Maths problems by assisting you with the right methods to solve problems and score full marks. You may still have doubts while referring to the Maths revision notes or Maths NCERT solutions. Solve those doubts by asking an expert through the “Undoubt” feature on the student dashboard.

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Chapter 9 - Differential Equations Exercise Ex. 9.1

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Chapter 9 - Differential Equations Exercise Ex. 9.2

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Chapter 9 - Differential Equations Exercise Ex. 9.3

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Chapter 9 - Differential Equations Exercise Ex. 9.4

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Let x and y be the x-coordinate and y-coordinate of the point on the curve respectively.

We know that the slope of a tangent to the curve in the coordinate axes is given by the relation,

 

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Chapter 9 - Differential Equations Exercise Ex. 9.5

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Chapter 9 - Differential Equations Exercise Ex. 9.6

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Chapter 9 - Differential Equations Exercise Misc. Ex.

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begin mathsize 14px style left parenthesis straight i right parenthesis space
x y equals a e to the power of x plus b e to the power of negative x end exponent plus x squared
Differentiating space both space sides space straight w. straight r. straight t space x space we space get
fraction numerator d left parenthesis x y right parenthesis over denominator d x end fraction equals a fraction numerator d over denominator d x end fraction open parentheses e to the power of x close parentheses plus b fraction numerator d over denominator d x end fraction open parentheses e to the power of negative x end exponent close parentheses plus fraction numerator d over denominator d x end fraction left parenthesis 2 x right parenthesis
rightwards double arrow x fraction numerator d y over denominator d x end fraction plus y equals a e to the power of x minus b e to the power of negative x end exponent plus 2 x
Again comma space differentiating space both space the space sides space straight w. straight r. straight t. space x comma space we space get
x fraction numerator d squared y over denominator d x squared end fraction plus fraction numerator d y over denominator d x end fraction plus fraction numerator d y over denominator d x end fraction equals a fraction numerator d over denominator d x end fraction left parenthesis e to the power of x right parenthesis minus b fraction numerator d over denominator d x end fraction left parenthesis e to the power of negative x end exponent right parenthesis plus 2 fraction numerator d over denominator d x end fraction left parenthesis x right parenthesis
rightwards double arrow x fraction numerator d squared y over denominator d x squared end fraction plus 2 fraction numerator d y over denominator d x end fraction equals a e to the power of x plus b e to the power of negative x end exponent plus 2
rightwards double arrow x fraction numerator d squared y over denominator d x squared end fraction plus 2 fraction numerator d y over denominator d x end fraction equals x y minus x squared plus 2
rightwards double arrow x fraction numerator d squared y over denominator d x squared end fraction plus 2 fraction numerator d y over denominator d x end fraction minus x y plus x squared minus 2 equals 0
Hence comma space the space given space function space is space straight a space solution space of space the space corresponding space differential space equation. end style

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Why CBSE Class 12 Science Maths solutions are important?

Maths is a subject which requires practising a variety of problems to understand concepts clearly. By solving as many problems as you can, you’ll be able to train your brain in thinking the logical way to solve maths problems. For practising problems, study materials such as sample papers, previous year papers, and NCERT solutions are needed.

Some of the best Maths experts work with us to give you the best solutions for Maths textbook questions and sample paper questions. Chapter-wise NCERT solutions for Class 12 Science Maths can be easily accessible on TopperLearning. Use these solutions to practise problems based on concepts such as direction ratios, probability, area between lines, inverse trigonometric functions, and more.

To prepare for your Maths exam, you need to attempt solving different kinds of Maths questions. One of the best ways to assess your problem-solving abilities is to attempt solving previous year papers with a set timer. Our Maths solutions will come in handy to help you with checking your answers and thus, improving your learning experience. So, to score more marks in your Class 12 board exams, use our Maths solutions that will enable you with the appropriate preparation.