AP EAMCET · Maths · Differential Equations
If \(a\) and \(b\) are respectively the order and degree of a differential equation \(y^2\left(y^{\prime \prime}\right)^2+3 x\left(y^{\prime}\right)^{1 / 3}+x^2 y^2=\sin x\), then
- A \(b=a\)
- B \(a=3 b\)
- C \(b=3 a\)
- D \(a b=6\)
Answer & Solution
Correct Answer
(C) \(b=3 a\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & (c) y^2 \cdot\left(y^{\prime \prime}\right)^2+3 x(y)^{1 / 3}+x^2 y^2=\sin x \\ & \Rightarrow\left(y^2 \cdot\left(y^{\prime \prime}\right)^2+x^2 \cdot y^2-\sin x\right)^3=27 x^3\left(y^{\prime}\right) \\ & \therefore \text { Order }=a=2, \text { Degree }=b=6 \\…
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
- The number of all four digit numbers which begin with 4 and end with either zero or five isAP EAMCET 2023 Easy
- \(\left|\begin{array}{ccc}1 & 1 & 1 \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3\end{array}\right|=\)AP EAMCET 2024 Medium
- If the equation of the hyperbola having \((8,3),(0,3)\) as foci and \(\frac{4}{3}\) as eccentricity is \(\frac{(x-\alpha)^2}{p}-\frac{(y-\beta)^2}{q}=1\) then \(p+q=\)AP EAMCET 2025 Medium
- If the probability function of a random variable \(\mathrm{X}\) is given by \(P(\mathrm{X}=k)=\frac{3^{c k}}{k !}\) for \(k=1,2,3, \ldots\) (where \(c\) is a constant), then \(c=\)AP EAMCET 2017 Easy
- If \(f(x)\) is a polynomial of the second degree in \(x\) such that \(f(0)=f(1)=3, f(2)=-3\). Then, \(\int \frac{f(x)}{x^3-1} d x=\)AP EAMCET 2020 Medium
- The general solution of the differential equation \(x d y-y d x=\sqrt{x^2+y^2} d x\) isAP EAMCET 2024 Medium
More PYQs from AP EAMCET
- If the engine of a long train moving with constant acceleration crosses a tree with velocity ' \(u\) ' and the last compartment of the train crosses the same tree with velocity ' \(v\) ', then the velocity with which the middle compartment crosses the same tree isAP EAMCET 2023 Hard
- The time period of a simple pendulum on the surface of the earth is T. The height above the surface of the earth at which the time period of the pendulum becomes \(2 \mathrm{~T}\) is (Radius of the earth \(=6400 \mathrm{~km}\) )AP EAMCET 2023 Medium
- The energy stored in a \(50 \mathrm{mH}\) inductor carrying a current of \(4 \mathrm{~A}\) isAP EAMCET 2020 Easy
- Which among the following is a possible product during cross aldol condensation between propanal (as electrophile) and butanal (as nucleophile)?AP EAMCET 2020 Hard
- The number of amphoteric oxides from the following is
\(\mathrm{CO}_2, \mathrm{GeO}_2, \mathrm{SnO}_2, \mathrm{PbO}_2, \mathrm{CO}, \mathrm{GeO}, \mathrm{SnO}, \mathrm{PbO}\)AP EAMCET 2025 Medium - If the differential equation obtained by eliminating A,B from \(y=\left(\sin ^{-1} x\right)^2+A \cos ^{-1} x+B\) is \(\left(a-x^2\right) y^{\prime \prime}-x y^{\prime}=b\), then \(\frac{b+a}{b-a}=\)AP EAMCET 2022 Medium