TS EAMCET · Maths · Differential Equations
If \(\cos x \frac{d y}{d x}=y \sin x-1, x \neq(2 n+1) \frac{\pi}{2}, n \in \mathrm{Z}\) is the differential equation corresponding to the curve \(y=f(x)\) and \(f(0)=1\) then \(f(x)=\)
- A \((1-x) \sec x\)
- B \((1-x) \cos x\)
- C \(x+\cos x\)
- D \(x+\sec x\)
Answer & Solution
Correct Answer
(A) \((1-x) \sec x\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x} - (\tan x) y = - \sec x\) IF \( = e^{\int -\tan x dx} = e^{\ln |\cos x|} = \cos x\) \(y \cos x = \int (-\sec x \cdot \cos x) dx\) \(y \cos x = \int -1 dx\) \(y \cos x = -x + C\) \(f(0)=1 \Rightarrow 1 \cdot \cos(0) = -0 + C \Rightarrow C=1\)…
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
- Let \(\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}\) be two non collinear vectors, \(\mathbf{O P}=x_1 \mathbf{a}+y_1 \mathbf{b}, \mathbf{O Q}=x_2 \mathbf{a}+y_2 \mathbf{b}\) and \(\mathbf{A}^{\prime} \mathbf{O}=\mathbf{O A}, \mathbf{B}^{\prime} \mathbf{O}=\mathbf{O B}\). If \(x_1=\frac{-3}{4}, x_2=\frac{1}{3}\), \(y_1=\frac{7}{4}, y_2=\frac{5}{3}\), thenTS EAMCET 2020 Easy
- If the d.r.'s of two lines are connected by the relations \(\mathrm{a}-\mathrm{b}+\mathrm{c}=0, \mathrm{a}^2-\mathrm{b}^2+2 \mathrm{c}^2=0\) and \(\theta\) is the angle between these lines then \(\cos \theta=\)TS EAMCET 2022 Medium
- If a function \(f\) is defined by \(f(x)=\frac{\cot ^3 x-\tan x}{\cos (x+\pi / 4)}(x \neq \pi / 4)\), then \(\lim _{x \rightarrow \frac{\pi}{4}} f(x)=\)TS EAMCET 2023 Easy
- If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+4 x^2-9 x-36\) \(=0\) and \(\alpha < \beta < \gamma\) then \(\alpha+2 \beta+3 \gamma=\)TS EAMCET 2023 Easy
- A bisector of the angle between the normals of the planes \(4 x+3 y=5\) and \(x+2 y+2 z=4\) is along the vectorTS EAMCET 2022 Easy
- If \(y=\log \left(x-\sqrt{x^2-1}\right)\), then \(\left(x^2-1\right) y^{\prime \prime}+x y^{\prime}+e^y+\sqrt{x^2-1}=\)TS EAMCET 2024 Easy
More PYQs from TS EAMCET
- A coil of resistance \(16 \Omega\) is placed with its plane perpendicular to a uniform magnetic field whose flux ( \(\phi\) in \(10^{-3}\) weber) changes with time ( t in second) as \(\phi=5 \mathrm{t}^2+4 \mathrm{t}+2\). The induced current at time \(t=6\) seconds isTS EAMCET 2025 Medium
- If the roots of the equation are and and the roots of the equation are , thenTS EAMCET 2018 Medium
- The value of \(c\) in the Lagrange's mean value theorem for \(f(x)=\sqrt{x-2}\) in the interval \([2,6]\) isTS EAMCET 2014 Medium
- A carrier wave of peak voltage is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index ofTS EAMCET 2021 Easy
- The following graph indicates the system containing 1 mole of gas involving various steps. When it moves from \(z\) to \(x\), the type of undergoing process is:
TS EAMCET 2021 Hard - The solution of the differential equation \(\sqrt{1-y^2} d x+x d y-\sin ^{-1} y d y=0\), isTS EAMCET 2019 Medium