NCERT Solutions for Differential Equations Exercise 9.6 Solutions

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Class 12 Maths NCERT Solutions Chapter 9 Differential Equations Exercise 9.6 is provided in the article. Class 12 Chapter 9 Differential Equations Exercises are based on solving the linear differential equations.

Download PDF: NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6

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CBSE CLASS XII Related Questions

  • 1.

    Find the value of \(x\) if \(A = B\), where

    \[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]


      • 2.

        Differential of \( \log \sin x \) with respect to \( \sqrt{\cos x} \) is :

          • \( -2\sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
          • \( \sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
          • \( \frac{2\sqrt{\cos x}}{\sin x} \)
          • \( \frac{1}{\sin x\sqrt{\cos x}} \)

        • 3.

          If \(y = \sqrt{\log \left\{ \sin \left( \dfrac{x^2}{3} + 1 \right) \right\}}\), then show that

          \[ \frac{dy}{dx} = \frac{x \cot \left( \dfrac{x^2}{3} + 1 \right)}{3y}. \]


            • 4.

              Solve the differential equation \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \).


                • 5.

                  The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

                    • \( \frac{7\pi}{12} \)
                    • \( \frac{5\pi}{12} \)
                    • \( -\frac{5\pi}{12} \)
                    • \( \frac{\pi}{3} \)

                  • 6.

                    Evaluate :

                    \[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

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