WBJEE · Maths · Differential Equations
The solution of \(\cos y \frac{d y}{d x}=e^{x+\sin y}+x^2 e^{\sin y}\) is \(f(x)+e^{-\sin y}=C\) (C is arbitrary real constant) where \(f(x)\) is equal to
- A \(e^x+\frac{1}{2} x^3\)
- B \(e^{-x}+\frac{1}{3} x^3\)
- C \(e^{-x}+\frac{1}{2} x^3\)
- D \(e^x+\frac{1}{3} x^3\)
Answer & Solution
Correct Answer
(D) \(e^x+\frac{1}{3} x^3\)
Step-by-step Solution
Detailed explanation
\(-e^{-\sin y} \cos y \frac{d y}{d x}=-\left[e^x+x^2\right] \Rightarrow d\left(e^{-\sin y}\right)+\left(e^x+x^2\right) d x=0 \Rightarrow e^{-\sin y}+e^x+\frac{x^3}{3}=C\)
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
- In a \(\triangle A B C\), tan \(A\) and \(\tan B\) are the roota \(p q\left(x^{2}+1\right)=r^{2} x\) Then, \(\Delta A B C\) isWBJEE 2014 Hard
- The number of all numbers having 5 digits, with distinct digits isWBJEE 2017 Easy
- The system of linear equations \(\lambda x+y+z=3\)
\(x-y-2 z=6\)
\(-x+y+z=\mu\) hasWBJEE 2012 Easy - Which of the following statements are true?WBJEE 2023 Easy
- The straight line through the origin which divides the area formed by the curves \(y=2 x-x^{2}, y=0\) and \(x=1\) into two equal halves isWBJEE 2021 Medium
- For all real values of \(a_{0}, a_{1}, a_{2}, a_{3}\) satisfying \(a_{0}+\frac{a_{1}}{2}+\frac{a_{z}}{3}+\frac{a_{3}}{4}=0,\) the equation \(a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}=0\) has a real root in the intervalWBJEE 2015 Hard
More PYQs from WBJEE
- A variable line passes through the fixed point \((\alpha, \beta) .\) The locus of the foot of the perpendicular from the origin on the line isWBJEE 2019 Medium
- The degree and order of the differential equation \(y=x\left(\frac{d y}{d x}\right)^2+\frac{d y}{d x}\) are respectivelyWBJEE 2011 Easy
- From the top of a tower, \(80 \mathrm{m}\) high from the ground, a stone is thrown in the horizontal direction with a velocity of \(8 \mathrm{ms}^{-1}\). The stone reaches the ground after a time \(t^{\prime}\) and falls at a distance of " \(\mathrm{d}\) ' from the foot of the tower. Assuming \(g=10 \mathrm{m} / \mathrm{s}^{2}\), the time \(t\) and distance d are given respectively byWBJEE 2012 Medium
- Same quantity of ice is filled in each of the two metal containers \(P\) and \(Q\) having the same size, shape and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in \(P\) melts completely in time \(t_{1}\) whereas in \(Q\) takes a time \(t_{2}\). The ratio of thermal conductivities of the materials of \(P\) and \(Q\) isWBJEE 2014 Medium
- If the vertices of a square are \(z_1, z_2, z_3\) and \(z_4\) taken in the anti-clockwise order, then \(z_3=\)WBJEE 2023 Medium
- A liquid of bulk modulus \(k\) is compressed by applying an external pressure such that its density increases by \(0.01 \% .\) The pressure applied on the liquid isWBJEE 2017 Easy