JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equations \(\frac{d y}{d x}+\frac{5}{x\left(x^5+1\right)} y=\frac{\left(x^5+1\right)^2}{x^7}, x > 0\). If \(y(1)=2\), then \(y(2)\) is equal to
- A \(\frac{637}{128}\)
- B \(\frac{679}{128}\)
- C \(\frac{693}{128}\)
- D \(\frac{697}{128}\)
Answer & Solution
Correct Answer
(C) \(\frac{693}{128}\)
Step-by-step Solution
Detailed explanation
Sol. I.F \(=e^{\int \frac{5 dx }{ x \left( x ^5+1\right)}}=e^{\int \frac{5 x ^{-6} dx }{\left( x ^{-5}+1\right)}}\) Put, \(1+ x ^{-5}= t \Rightarrow-5 x ^{-6} dx = dt\) \(\Rightarrow e^{\int \frac{-d t}{t}}=\frac{1}{t}=\frac{x^5}{1+x^5}\)…
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 \(A =\left[\begin{array}{ccc}2 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & -1 & 0\end{array}\right]\) and \(B = A - I\). If \(\omega=\frac{\sqrt{3} i -1}{2}\) then the number of elements in the set \(\left\{ n \in\{1,2, \ldots, 100\}: A ^{ n }+(\omega B )^{ n }= A + B \right\}\) is equal to \(..........\)JEE Mains 2022 Hard
- The number of ways five alphabets can be chosen from the alphabets of the word \(MATHEMATICS\), where the chosen alphabets are not necessarily distinct, is equal to :JEE Mains 2024 Hard
- The area of the region enclosed by the curves \(y=\mathrm{e}^x, y=\left|\mathrm{e}^x-1\right|\) and \(y\)-axis is:JEE Mains 2025 Medium
- If \(\lim _{x \rightarrow 0} \frac{\alpha x e^{x}-\beta \log _{e}(1+x)+\gamma x^{2} e^{-x}}{x \sin ^{2} x}=10, \alpha, \beta, \gamma \in R\), then the value of \(\alpha+\beta+\gamma\) is \(......\)JEE Mains 2021 Hard
- If \(f: \mathbf{N} \rightarrow \mathbf{Z}\) is defined by
\(f(n) = \begin{vmatrix} n & -1 & -5 \\ -2n^2 & 3(2k+1) & 2k+1 \\ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix}\), \(k \in \mathbf{N}\),
and \(\sum_{n=1}^{k} f(n) = 98\), then \(k\) is equal to :JEE Mains 2026 Hard - For \(\alpha, \beta, \gamma, \in \mathbf{R}\), if \(\lim _{x \rightarrow 0} \frac{x^2 \sin \alpha x+(\gamma-1) e^{x^2}}{\sin 2 x-\beta x}=3\), then \(\beta+\gamma-\alpha\) is equal to:JEE Mains 2025 Easy
More PYQs from JEE Mains
- The values of \('a'\) for which one root of the equation \(x^2 - (a +1)\,x + a^2 + a - 8 = 0\) exceeds \(2\) and the other is lesser than \(2\), are given byJEE Mains 2013 Hard
- Let \(P\) be a point on the parabola, \(x^2 = 4y.\) If the distance of \(P\) from the centre of the circle, \(x^2 + y^2 + 6x + 8 = 0\) is minimum, then the equation of the tangent to the parabola at \(P,\) isJEE Mains 2018 Hard
- If \({\Delta _r} = \left| {\begin{array}{*{20}{c}}
r&{2r - 1}&{3r - 2} \\
{\frac{n}{2}}&{n - 1}&a \\
{\frac{1}{2}n\left( {n - 1} \right)}&{{{\left( {n - 1} \right)}^2}}&{\frac{1}{2}\left( {n - 1} \right)\left( {3n - 4} \right)}
\end{array}} \right|\) then the value of \(\sum\limits_{r = 1}^{n - 1} {{\Delta _r}} \)JEE Mains 2014 Hard - Let \(q\) be the maximum integral value of \(p\) in \([0,10]\) for which the roots of the equation \(x ^2- px +\frac{5}{4} p =0\) are rational. Then the area of the region \(\{(x, y): 0 \leq y\) \(\left.\leq(x-q)^2, 0 \leq x \leq q\right\}\) isJEE Mains 2023 Hard
- The area (in sq. units) of the region \(\left\{(\mathrm{x}, \mathrm{y}) \in \mathrm{R}^{2}: \mathrm{x}^{2} \leq \mathrm{y} \leq 3-2 \mathrm{x}\right\},\) isJEE Mains 2020 Hard
- If the tangent to the curve \(y\, = \,\frac{x}{{{x^2}\, - \,3}},\,x\, \in \,R,\,(x\, \ne \, \pm \,\sqrt 3 )\) at a point \((\alpha ,\,\beta )\,\ne\,(0,0)\) on it is parallel to the line \(2x + 6y -11 = 0\) thenJEE Mains 2019 Hard