JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \(\sec \mathrm{x} d \mathrm{y}+\{2(1-\mathrm{x}) \tan \mathrm{x}+\mathrm{x}(2-\mathrm{x})\}\) \(\mathrm{dx}=0\) such that \(\mathrm{y}(0)=2\). Then \(\mathrm{y}(2)\) is equal to :
- A \(2\)
- B \(2\{1-\sin (2)\}\)
- C \(2\{\sin (2)+1\}\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=2(x-1) \sin x+\left(x^2-2 x\right) \cos x\) Now both side integrate \( y(x)=\int 2(x-1) \sin x d x+\left[\left(x^2-2 x\right)(\sin x)-\int(2 x-2) \sin x d x\right] \) \( y(x)=\left(x^2-2 x\right) \sin x+\lambda\) \( y(0)=0+\lambda \Rightarrow 2=\lambda\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The integral \(\int_{\pi /6}^{\pi /3} {{{\sec }^{2/3}}\,x\,\,\cos e{c^{4/3}}\,x\,dx} \) is equal toJEE Mains 2019 Hard
- Let \(f: R \rightarrow R\) be defined as \(f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), & \text { if } x<-1 \\ \left|a x^{2}+x+b\right|, & \text { if }-1 \leq x \leq 1 \\ \sin (\pi x), & \text { if } x>1\end{array}\right.\) If \(f(x)\) is continuous on \(R,\) then \(a+b\) equals ..... .JEE Mains 2021 Hard
- If \(f\left( x \right) = \frac{{2 - x\,\cos \,x}}{{2 + x\,\cos \,x}}\) and \(g\left( x \right) = {\log _e}\,x\), \(\left( {x > 0} \right)\) then the value of the integral \(\int\limits_{\frac{{ - \pi }}{4}}^{\frac{\pi }{4}} {g\left( {f\left( x \right)} \right)} dx\) isJEE Mains 2019 Hard
- Let \(z_1, z_2\) and \(z_3\) be three complex numbers on the circle \(|z|=1\) with \(\arg \left(z_1\right)=\frac{-\pi}{4}, \arg \left(z_2\right)=0\) and \(\arg \left(z_3\right)=\frac{\pi}{4}\). If \(\left|z_1 \bar{z}_2+z_2 \bar{z}_3+z_3 \bar{z}_1\right|^2=\alpha+\beta \sqrt{2}, \alpha, \beta \in \mathbf{Z}\), then the value of \(\alpha^2+\beta^2\) is :JEE Mains 2025 Medium
- The slope of tangent at any point \((x, y)\) on a curve \(y = y ( x )\) is \(\frac{x^2+y^2}{2 x y},x > 0\). If \(y(2)=0\), then a value of \(y(8)\) isJEE Mains 2023 Hard
- If a curve \(y=y(x)\) passes through the point \(\left(1, \frac{\pi}{2}\right)\) and satisfies the differential equation \(\left(7 x^4 \cot y-e^x \operatorname{cosec} y\right) \frac{d x}{d y}=x^5, x \geq 1\), then at \(x=2\), the value of cosy is:JEE Mains 2025 Medium
More PYQs from JEE Mains
- Let the line passing through the points, \(P(2,-1,2)\) and \(Q(5,3,4)\) meet the plane \(x-y+z=4\) at the point \(R\). Then the distance of the point \(R\) from the plane \(x+2 y+3 z+2=0\) measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal toJEE Mains 2023 Hard
- If \(\vec{a}\) and \(\vec{b}\) are two vectors such that \(|\vec{a}| = 2\) and \(|\vec{b}| = 3\), then the maximum value of \(3\left|\left(3\vec{a} + 2\vec{b}\right)\right| + 4\left|\left(3\vec{a} - 2\vec{b}\right)\right|\) is :JEE Mains 2026 Hard
- The function \(f(x)=\frac{4 x^{3}-3 x^{2}}{6}-2 \sin x+(2 x-1) \cos x\)JEE Mains 2021 Hard
- Let \( y=y(x) \) be the solution curve of the differential equation \( (1+x^{2})dy+(y-\tan^{-1}x)dx=0, \) \( y(0)=1 \). Then the value of \( y(1) \) is:JEE Mains 2026 Medium
- Consider a set of \(3 n\) numbers having variance \(4.\) In this set, the mean of first \(2 n\) numbers is \(6\) and the mean of the remaining \(n\) numbers is \(3.\) A new set is constructed by adding \(1\) into each of first \(2 n\) numbers, and subtracting \(1\) from each of the remaining \(n\) numbers. If the variance of the new set is \(k\), then \(9 k\) is equal to .... .JEE Mains 2021 Hard
- Let \(\mathrm{y}=\mathrm{y}(\mathrm{x})\) be the solution of the differential equation \(\left((x+2) e^{\left(\frac{y+1}{x+2}\right)}+(y+1)\right) d x=(x+2) d y, y(1)=1\) If the domain of \(y=y(x)\) is an open interval \((\alpha, \beta)\), then \(|\alpha+\beta|\) is equal to \(......\)JEE Mains 2021 Hard