JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \(x d y=\left(y+x^{3} \cos x\right) d x\) with \(y(\pi)=0\) then \(y\left(\frac{\pi}{2}\right)\) is equal to :
- A \(\frac{\pi^{2}}{2}-\frac{\pi}{4}\)
- B \(\frac{\pi^{2}}{4}+\frac{\pi}{2}\)
- C \(\frac{\pi^{2}}{4}-\frac{\pi}{2}\)
- D \(\frac{\pi^{2}}{2}+\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi^{2}}{4}+\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(x d y=\left(y+x^{3} \cos x\right) d x\) \(x d y=y d x+x^{3} \cos x d x\) \(\frac{x d y-y d x}{x^{2}}=\frac{x^{3} \cos x d x}{x^{2}}\) \(\int \frac{d}{d x}\left(\frac{y}{x}\right) d x=\int x \cos x d x\) \(\Rightarrow \frac{y}{x}=x \sin x-\int 1 \cdot \sin x d x\)…
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
- Let the coefficients of three consecutive terms in the binomial expansion of \((1+2 x)^{ n }\) be in the ratio \(2: 5: 8\). Then the coefficient of the term, which is in the middle of these three terms, is \(...........\).JEE Mains 2023 Hard
- Let \(z = a +i b , b \neq 0\) be complex numbers satisfying \(z ^{2}=\overline{ Z } \cdot 2^{1-|z|}\). Then the least value of \(n\) \(\in N\), such that \(z ^{ n }=( z +1)^{ n }\), is equal to.JEE Mains 2022 Hard
- \(\sum_{\substack{i, j=0 \\ i \neq j}}^{n}{ }^{n} C_{i}{ }^{n} C_{j}\) is equal toJEE Mains 2022 Hard
- If the circle \(x^2 + y^2 - 6x - 8y + (25 - a^2)\, = 0\) touches the axis of \(x\), then \(a\) equalsJEE Mains 2013 Hard
- Let \(\left\{a_{n}\right\}_{n-1}^{\infty}\) be a sequence such that \(a_{1}=1, a_{2}=1\) and \(a_{n+2}=2 a_{n+1}+a_{n}\) for all \(n \geq 1 .\) Then tha value of \(47 \sum_{n=1}^{\infty} \frac{a_{n}}{2^{3 n}}\) is equal to \(.....\)JEE Mains 2021 Hard
- Let \(\overrightarrow{ a }\) be a non-zero vector parallel to the line of intersection of the two planes described by \(\hat{i}+\hat{j}, \hat{i}+\hat{k}\) and \(\hat{i}-\hat{j}, \hat{j}-\hat{k}\). If \(\theta\) is the angle between the vector \(\vec{a}\) and the vector \(\vec{b}=2 \hat{i}-2 \hat{j}+\hat{k}\) and \(\vec{a} \cdot \vec{b}=6\) then the ordered pair \((\theta,|\vec{a} \times \vec{b}|)\) is equal toJEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \(A=\left[\begin{array}{ll}2 & 3 \\ a & 0\end{array}\right], a \in R\) be written as \(P+Q\) where \(P\) is a symmetric matrix and \(Q\) is skew symmetric matrix. If \(\operatorname{det}(Q)=9\), then the modulus of the sum of all possible values of determinant of \(P\) is equal to:JEE Mains 2021 Medium
- If \(\tan \left(\frac{\pi}{9}\right), x, \tan \left(\frac{7 \pi}{18}\right)\) are in arithmetic progression and \(\tan \left(\frac{\pi}{9}\right), y, \tan \left(\frac{5 \pi}{18}\right)\) are also in arithmetic progression, then \(|x-2 y|\) is equal to:JEE Mains 2021 Hard
- Let a circle \(C\) in complex plane pass tltrough the points \(z _{1}=3+4 i , z _{2}=4+3 i\) and \(z _{3}=5 i\). If \(z \left(\neq z _{1}\right)\) is a point on \(C\) such that the line through \(z\) and \(z _{1}\) is perpendicular to the line through \(z _{2}\) and \(z _{3}\), then \(\arg ( z )\) is equal toJEE Mains 2022 Hard
- A variable \(X\) takes values \(0, 0, 2, 6, 12, 20, \ldots, n(n-1)\) with frequencies \({}^nC_0, {}^nC_1, {}^nC_2, {}^nC_3, {}^nC_4, {}^nC_5, \ldots, {}^nC_n\), respectively. If the mean of this data is \(60\), then its median is :JEE Mains 2026 Hard
- Let a variable line of slope \(m>0\) passing through the point \((4,-9)\) intersect the coordinate axes at the points \(A\) and \(B\). the minimum value of the sum of the distances of \(\mathrm{A}\) and \(\mathrm{B}\) from the origin isJEE Mains 2024 Hard
- Let \(M\) be any \(3 \times 3\) matrix with entries from the set \(\{0,1,2\}\). The maximum number of such matrices, for which the sum of diagonal elements of \(M ^{ T } M\) is seven, is .............JEE Mains 2021 Medium