WBJEE · Maths · Differential Equations
If \(y=\frac{x}{\log _e|c x|}\) is the solution of the differential equation \(\frac{d y}{d x}=\frac{y}{x}+\phi\left(\frac{x}{y}\right)\), then \(\phi\left(\frac{x}{y}\right)\) is given by
- A \(\frac{y^2}{x^2}\)
- B \(-\frac{y^2}{x^2}\)
- C \(\frac{x^2}{y^2}\)
- D \(-\frac{x^2}{y^2}\)
Answer & Solution
Correct Answer
(B) \(-\frac{y^2}{x^2}\)
Step-by-step Solution
Detailed explanation
Hint : \(y=\frac{x}{\ell n|c x|}\)…
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
- If \(\omega\) is an imaginary cube root of unity, then the value of the determinant \(\left|\begin{array}{ccc}1+\omega & 0 & -\omega \\ 1+\omega^{2} & \omega & -\omega^{2} \\ \omega+\omega^{2} & \omega & -\omega^{2}\end{array}\right|\) isWBJEE 2015 Medium
- Given \(\frac{d^2 y}{d x^2}+\cot x \frac{d y}{d x}+4 y \operatorname{cosec}^2 x=0\). Changing the independent variable \(x\) to \(z\) by the substitution \(z=\log \tan \frac{x}{2}\), the equation is changed toWBJEE 2023 Hard
- A straight line through the point (3,-2) is ndined at an angle \(60^{\circ}\) to the line \(\sqrt{3} x+y=1\). If it intersects the \(X\) -axis, then its equation vill beWBJEE 2019 Medium
- If \(a, b, c\) are in G.P. \((a>1, b>1, c>1)\), then for any real number \(x(\) with \(x>0, x \neq 1), \log _{\mathrm{a}} x, \log _{\mathrm{b}} x, \log _{\mathrm{c}} x\) are inWBJEE 2009 Hard
- The general solution of the different equation \(100 \frac{\mathrm{d}^2 \mathrm{y}}{\mathrm{dx}^2}-20 \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0\) isWBJEE 2010 Hard
- If \(a, b, c\) are in G. P. and \(\log a .-\log 2 b, \log 2 b-\log 3 c, \log 3 c-\log a\) are in A. P., then \(a, b, c\) are the lengths of the sides of a triangle which isWBJEE 2022 Hard
More PYQs from WBJEE
- The equation \(\sqrt{3} \sin x+\cos x=4\) hasWBJEE 2009 Medium
- A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation ( \(T\) ) of the liquid drop depends on radius \((n\) of the drop, density \((\rho)\) and surface tension (5) of the liquid. Which among the following will be a possible expression for \(T\) (where, \(k\) is a dimensionless constant)?WBJEE 2018 Medium
- Let \(x_{1}, x_{2}\) be the roots of \(x^{2}-3 x+a=0\) and \(x_{3}, x_{4}\) be the roots of \(x^{2}-12 x+b=0\) If \(x_{1} < x_{2} < x_{3} < x_{4}\) and \(x_{1}, x_{2}, x_{3}, x_{4}\) are in GP. then ab equalsWBJEE 2019 Easy
- The general solution of the differential equation \(\frac{d y}{d x}=\frac{x+y+1}{2 x+2 y+1}\) isWBJEE 2012 Hard
- If \(\Delta(x)=\left|\begin{array}{ccc}x-2 & (x-1)^2 & x^3 \\ x-1 & x^2 & (x+1)^3 \\ x & (x+1)^2 & (x+2)^3\end{array}\right|\), then coefficient of \(x\) in \(\Delta(x)\) isWBJEE 2022 Medium
- Let \(f\) be any continuously differentiable function on \([a, b]\) and twice differentiable on \((a, b)\) such that \(f(a)=f^{\prime}(a)=0\) and \(f(b)=0\) Then.WBJEE 2015 Easy