TS EAMCET · Maths · Differential Equations
If the solution of the differential equation \(x y^{\prime}=y+x^2 \sin x\) subject to the condition \(y(\pi)=0\) is \(y=f(x)\) and \(f(x)\) has an extreme value at \(x=\alpha\), then
- A \(\alpha \cos \alpha+2\)
- B \(\alpha=(2 n-1) \frac{\pi}{2}, n \in Z\)
- C \(\cos \frac{\alpha}{2}=1\)
- D \(\alpha=\cot \frac{\alpha}{2}\)
Answer & Solution
Correct Answer
(D) \(\alpha=\cot \frac{\alpha}{2}\)
Step-by-step Solution
Detailed explanation
Given differential equation, \(\begin{aligned} x \frac{d y}{d x}-y & =x^2 \sin x \\ \Rightarrow \quad \frac{x d y-y d x}{x^2} & =\sin x d x \Rightarrow \int d\left(\frac{y}{x}\right)=\int \sin x d x \\ \Rightarrow \quad \frac{y}{x} & =-\cos x+c\end{aligned}\)…
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
- If the eccentricity of a conic satisfies the equation , then that conic isTS EAMCET 2018 Medium
- The shortest distance between the line \(\mathbf{r}=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}+\lambda(\hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}})\) and the plane \(\mathbf{r} \cdot(\hat{\mathbf{i}}+5 \hat{\mathbf{j}}+\hat{\mathbf{k}})=5\) isTS EAMCET 2020 Easy
- The sum of all the roots of the equation \(\left|\begin{array}{ccc}x & -3 & 2 \\ -1 & -2 & (x-1) \\ 1 & (x-2) & 3\end{array}\right|=0\) isTS EAMCET 2025 Medium
- If \(Z_1=\sqrt{3}+i \sqrt{3}\) and \(Z_2=\sqrt{3}+i\), and \(\left(\frac{Z_1}{Z_2}\right)^{50}=x+i y\), then the point \((x, y)\) lies inTS EAMCET 2024 Hard
- If \(\int x^3 \sin 3 x d x=\frac{1}{27}[f(x) \cos 3 x+g(x) \sin 3 x]+\mathrm{c}\) then \(f(1)+g(1)=\)TS EAMCET 2025 Medium
- The roots of the equation \(x^3-3 x^2+3 x+7=0\) are \(\alpha\), \(\beta, \gamma\) and \(\omega, \omega^2\) are complex cube roots of unity. If the terms containing \(x^2\) and \(x\) are missing in the transformed equation when each one of these roots is decreased by \(h\), then \(\frac{\alpha-h}{\beta-h}+\frac{\beta-h}{\gamma-h}+\frac{\gamma-\mathrm{h}}{\alpha-\mathrm{h}}=\)TS EAMCET 2024 Hard
More PYQs from TS EAMCET
- Let \(P(2,4), Q(18,-12)\) be the points on the parabola \(y^2=8 x\). The equation of straight line having slope \(\frac{1}{2}\) and passing through the point of intersection of the tangents to the parabola drawn at the points \(P\) and \(Q\) isTS EAMCET 2018 Medium
- The acute angle between the curves \(y=3 x^2-2 x-1\) and \(y=x^3-1\) at their point of intersection which lies in the first quadrant isTS EAMCET 2025 Medium
- The number of non-real roots of the equation \(x^{10}-3 x^8+5 x^6-5 x^4+3 x^2-1=0\) isTS EAMCET 2022 Medium
- The energy required to take a body from the surface of the earth to a height equal to the radius of the earth is ' \(W\) '. The energy required to take this body from the surface of the earth to a height equal to twice the radius of the earth isTS EAMCET 2024 Hard
- The equation of pair of lines passing through origin and forming an equilateral triangle with the line \(3 x+4 y-5=0\) isTS EAMCET 2018 Medium
- Consider the four points \(A(1,-2,-1)\), \(B(4,0,-3), C(1,2,-1)\) and \(D(2,-4,-5)\) in space. If \(\mathbf{b}=\mathbf{A B}, \mathbf{c}=\mathbf{A C}\) and \(\mathbf{d}=\mathbf{A D}\), thenTS EAMCET 2021 Hard