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RS Aggarwal Class 12 Solutions Chapter-19 Differential Equations with Variable Separable

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Last updated date: 22nd Mar 2024
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Class 12 RS Aggarwal Chapter-19 Differential Equations with Variable Separable Solutions - Free PDF Download

When it comes to board exams especially for the students of class 12, sometimes, they need some help in understanding some concepts in the subject of Mathematics. The RS Aggarwal Solutions Class 12 differential equations with variable separable is meant to provide all the assistance that they need to score some high marks in the examinations and that too in the best way. These solutions that are provided by us to the students are meant to increase their knowledge about the concepts of every single chapter. With the help of our RS Aggarwal solutions Class 12 chapter 19, students can understand the concepts in a better way and hence will be able to score higher marks in their exams. These solutions are very easy to download and will provide much-needed help to them for their preparation. 


Mathematics has always played a significant role in human lives. Everyone, regardless of their knowledge of mathematical concepts, uses mathematics in a variety of ways in their daily lives. When it comes to pursuing your career, your 12th-grade education is crucial. Mathematics Class 12th Solutions by RS Aggarwal provides students with the ideal look at the mechanism that allows them to comprehend the complexities of Mathematics quickly. By studying the RS Aggarwal Solutions, students can build a strong foundation in mathematics and put themselves in a position to deal with the most difficult questions in class 12th mathematics.


The syllabus for RS Aggarwal Class 12th Maths book is divided into 33 chapters. All of the chapters provide in-depth coverage of the advanced concepts tested in high-level entrance exams such as the JEE, BITSAT, NEET, and others. You will find RS Aggarwal's solutions to be very reliable because they have been written by CBSE guidelines. Calculus, Determinants, Coordinate Geometry, and Statistics are all important topics that have been covered in detail under various headings.

Competitive Exams after 12th Science

Real Life Applications of Differential Equations

Differential equations are used in a variety of disciplines, including applied science, mathematics, and engineering. Apart from technical applications, they are also used to solve a variety of real-life concerns. Let's look at some real-time applications of differential equations:

  • Differential equations are used to describe the growth and decay of various exponential functions.

  • They're also used to show how a return on investment has changed over time.

  • They are applied in the field of medical science to represent cancer growth and illness spread in the body.

  • These equations can also be used to explain the motion of waves or a pendulum.

  • It can also be used to describe the movement of electricity.

  • They support economists in determining the best investment strategy.

  • Other technical uses include: ­ heat conduction analysis, and in physics, it may be used to explain wave motion.


Types of Differential Equations

Differential equations are classified based on a variety of variables including order, type, linearity, and homogeneity. 


Based on The Type of Variables, The Differential Equation Types are:

  • Ordinary Differential Equations: Ordinary differential equations are those with only one independent variable.

  • Partial Differential Equations: These are the types of differential equations in which the dependent variable is influenced by two or more independent variables.

Differential Equation types are classified based on the order of the equations and those are:

  • First order differential equation: The derivative's highest power is one. 

  • Second order differential equation: The derivative's highest power is two.

  • Nth order differential equation: Any number 'n' can be the largest power of the derivative.

The following is a list of differential equations based on their linearity:

  • Linear differential equations: These are differential equations where the variable's power is always one.

  • Nonlinear differential equations: Differential equations with any number other than 1 as the power of the variables in the equation.

Based on Homogeneity, the Differential Equation types are:

  • Homogeneous differential equations

  • Non homogeneous differential equations


The Solution of Differential Equations

The general solution of the deferential solution is the correlation between the variables x and y that is obtained when the derivatives are removed, and the relation contains arbitrary constants to reflect the order of an equation. The first order differential equation solution has one arbitrary constant, whereas the second order differential equation solution contains two arbitrary constants. When arbitrary constants are given specified values, the general solution of the differential equation is obtained. Some common forms are given to derive the general solution to the first order differential equation of first degree, as follows:

  • Homogeneous Equation

  • Non homogeneous differential equations

  • Linear Equation 

  • Exact Differential Equation

  • Variable desperate method


Fundamental principles of differential equations

  • The derivatives of the dependent variable with regard to only one independent variable are used in the Ordinary Differential Equation. F(x, y, y',...., yn-1) = yn is the formula for ordinary differential equations.

  • There are derivatives for more than one independent variable in a partial differential equation. 

  • The partial differential equation has the formula ∂u/∂x (x,y) = 0

  • The highest order derivative of the dependent variable with respect to the independent variable determines the order of a differential equation.

  • A first-order linear differential equation has the form dy/dx +Py Q, with P and Q being constants or functions of just x.

  • A function that satisfies the specified differential equation is referred to as a solution.


Conclusion:

On Vedantu, you can find RS Aggarwal Class 12 solution in PDF format, which you can download for free. When it comes to getting the most accurate study materials, Vedantu is a name you can trust. You can attend free live masterclasses and download PDFs of study materials and solutions using the Vedantu learning app. Students can use the subject-specific solutions in a chapter-by-chapter and exercise-by-exercise format to get their questions answered quickly. The more you practise, the better your command of the subject will become.

FAQs on RS Aggarwal Class 12 Solutions Chapter-19 Differential Equations with Variable Separable

1. Where Will I be Able to Download RS Aggarwal Class 12 Chapter 19 Solutions?

All you need to do is visit the official site of Vedantu in order to get your hands to the RS Aggarwal Class 12 Maths Chapter 19 solutions right now. These solutions are available in PDF Format and will definitely be a great help when you need to prepare for your board exams for class 12. That is why students always opt for Vedantu when they need some preparation help for their exams.

2. Does RS Aggarwal Class 12 Chapter 19 Maths Solutions Help in Preparation?

Yes, RS Aggarwal Class 12 Maths Chapter 19 solutions are very helpful when it comes to exam preparation.

3. How Can One Download the Solutions for RS Aggarwal Class 12 Chapter 19 Notes?

Students need to visit the official website of Vedantu in order to find the solutions for Class 12 Maths Chapter 19 by RS Aggarwal.