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# Differential Equations

At Saralstudy, we are providing you with the solution of Class 12th mathematics Differential Equations according to the latest NCERT (CBSE) Book guidelines prepared by expert teachers. Here we are trying to give you a detailed answer to the questions of the entire topic of this chapter so that you can get more marks in your examinations by preparing the answers based on this lesson. We are trying our best to give you detailed answers to all the questions of all the topics of Class 12th mathematics Differential Equations so that you can prepare for the exam according to your own pace and your speed.

In this chapter, we will shidy about differential equations and their solutions. Concepts of differential equations will help us in this class and also in higher studies. It has many applications in other branches like science, algebra, etc. Key topics of this chapter are - definition, order and degree, general and particular solutions, formation of differential equaňon whose general solution is given, method of separation of variables, homogeneous differential equations of first order and degree.

Download pdf of NCERT Solutions for Class mathematics Chapter 9 Differential Equations

Download pdf of NCERT Examplar with Solutions for Class mathematics Chapter 9 Differential Equations

### Exercise 1

•  Q1 Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align} Q2 Determine order and degree(if defined) of differential equation y' + 5y = 0 Q3 Determine order and degree(if defined) of differential equation \begin{align}\left(\frac{ds}{dt}\right)^4\;+\;3s\frac{d^2s}{dt^2}\;=\;0\end{align} Q4 Determine order and degree(if defined) of differential equation \begin{align}\left(\frac{d^2y}{dx^2}\right)^2\;+\;cos\left(\frac{dy}{dx}\right)\;=\;0\end{align} Q5 Determine order and degree(if defined) of differential equation \begin{align}\frac{d^2y}{dx^2}=\cos3x  + sin3x\end{align} Q6 Determine order and degree(if defined) of differential equation (ym)2 + (yn)3 + (y')4 + y5 =0 Q7 Determine order and degree(if defined) of differential equation ym + 2yn + y' =0 Q8 Determine order and degree(if defined) of differential y' + y =ex Q9 Determine order and degree(if defined) of differential equation yn + (y')2 + 2y =0 Q10 Determine order and degree(if defined) of differential equation yn + 2y' + siny = 0 Q11 The degree of the differential equation \begin{align}\left(\frac{d^2y}{dx^2}\right)^3\;+ \left(\frac{dy}{dx}\right)^2+\;sin\left(\frac{dy}{dx}\right)\;+ 1=\;0\end{align} is (A) 3 (B) 2 (C) 1 (D) not defined Q12 The order of the differential equation \begin{align}2x^2\frac{d^2y}{dx^2}\;- \;3\frac{dy}{dx}\;+ y=\;0\end{align} is (A) 2 (B) 1 (C) 0 (D) not defined

### Exercise 2

•  Q1 y = ex +1 : yn -y' = 0 Q2 y = x2 + 2x + C : y' - 2x - 2 = 0 Q3 y = cosx + C : y' + sinx = 0 Q4 \begin{align} y= \sqrt{1+x^2} : y^{'}=\frac{xy}{1+x^2}\end{align} Q5 y = Ax : xy' = y (x ≠ 0) Q6 \begin{align} y = xsinx:xy{'}=y +x\sqrt{x^2 -y^2}(x\neq0\; and\; x>y\; or\; x<-y)\end{align}

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