JEE Mains · Maths · STD 12 - 9. differential equations
If \(y=y(x)\) is the solution curve of the differential equation \(\frac{d y}{d x}+y \tan x=x \sec x, \quad 0 \leq x \leq \frac{\pi}{3}\), \(y (0)=1\), then \(y \left(\frac{\pi}{6}\right)\) is equal to
- A \(\frac{\pi}{12}-\frac{\sqrt{3}}{2} \log _e\left(\frac{2}{e \sqrt{3}}\right)\)
- B \(\frac{\pi}{12}+\frac{\sqrt{3}}{2} \log _{ e }\left(\frac{2 \sqrt{3}}{ e }\right)\)
- C \(\frac{\pi}{12}-\frac{\sqrt{3}}{2} \log _{ e }\left(\frac{2 \sqrt{3}}{ e }\right)\)
- D \(\frac{\pi}{12}+\frac{\sqrt{3}}{2} \log _{ e }\left(\frac{2}{ e \sqrt{3}}\right)\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{12}-\frac{\sqrt{3}}{2} \log _e\left(\frac{2}{e \sqrt{3}}\right)\)
Step-by-step Solution
Detailed explanation
Here I.F. \(=\sec x\) Then solution of D.E : \(y(\sec x)=x \tan x-\ln (\sec x)+c\) \(\text { Given } y(0)=1 \Rightarrow c=1\) \(\therefore \quad y(\sec x)=x \tan x-\ln (\sec x)+1\)…
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 area of the region \(\left\{(x, y): x^2 \leq y \leq\left|x^2-4\right|, y \geq 1\right\}\) isJEE Mains 2023 Hard
- If \(2\) and \(6\) are the roots of the equation \(a x^2+b x+1=0\), then the quadratic equation, whose roots are \(\frac{1}{2 a+b}\) and \(\frac{1}{6 a+b}\), is :JEE Mains 2024 Medium
- Let a circle \(C\) have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of \(C\) on the line \(x + y = 1\) is \(\sqrt{14}\), then the square of the radius of \(C\) is _______.JEE Mains 2026 Hard
- If \(f : R \rightarrow R\) be a continuous function satisfying \(\int \limits_0^{\pi / 2} f(\sin 2 x) \cdot \sin x d x+\alpha \int \limits_0^{\pi / 4} f(\cos 2 x) \cdot \cos x d x=0\)then \(\alpha\) is equal toJEE Mains 2023 Hard
- The sum of all the four-digit numbers that can be formed using all the digits \(2,1,2,3\) is equal to \(.......\).JEE Mains 2023 Hard
- Let \(9 < x_1 < x_2 < \ldots < x_7\) be in an \(A.P.\) with common difference \(d\). If the standard deviation of \(x_1, x_2 \ldots\), \(x _7\) is \(4\) and the mean is \(\overline{ x }\), then \(\overline{ x }+ x _6\) is equal to:JEE Mains 2023 Hard
More PYQs from JEE Mains
- If \(f(x)=\left\{\begin{array}{ccc}\frac{1}{|x|} & ; & |x| \geq 1 \\ a x^{2}+b & ; & |x|<1\end{array}\right.\) is differentiable at every point of the domain, then the values of \(a\) and \(b\) are respectivelyJEE Mains 2021 Hard
- Let \(\vec a\, = \,\hat i\, + \,\hat j\, + \,\sqrt 2 \hat k,\,\,\vec b\, = \,{b_1}\hat i\, + \,{b_2}\hat j\, + \sqrt 2 \hat k\) and \(\vec c\, = \,5\hat i\, + \,\hat j + \sqrt 2 \hat k\) be three vectors such that the projection vector of \(\vec b\) on \(\vec a\) is \(\vec a\). If \(\vec a\, + \vec b\) is perpendicular to \(\vec c\) , then \(\left| {\vec b} \right|\) is equal toJEE Mains 2019 Hard
- Let \(A\,(4, -4)\) and \(B\,(9,6)\) be points on the parabola \(y^2 = 4x\) . Let \(C\) be chosen on the arc \(AOB\) of the parabola, where \(O\) is the origin, such that the area of \(\Delta ACB\) is maximum. Then, the area (in sq. units) of \(\Delta ACB,\) isJEE Mains 2019 Hard
- For real numbers \(\alpha\) and \(\beta\), consider the following system of linear equations: \(x+y-z=2, x+2 y+\alpha z=1,2 x-y+z=\beta\). If the system has infinite solutions, then \(\alpha+\beta\) is equal to \(.....\)JEE Mains 2021 Medium
- The area (in sq. units) of the region bounded by the parabola, \(y = x^2 + 2\) and the lines, \(y = x + 1, x = 0\) and \(x = 3\), isJEE Mains 2019 Hard
- Let \(S =\{\sqrt{ n }: 1 \leq n \leq 50\) and \(n\) is odd \(\}\) Let \(a \in S\) and \(A =\left[\begin{array}{ccc}1 & 0 & a \\ -1 & 1 & 0 \\ - a & 0 & 1\end{array}\right]\) If \(\sum_{ a \in S } \operatorname{det}(\operatorname{adj} A )=100 \lambda\), then \(\lambda\) is equal toJEE Mains 2022 Medium