MHT CET · Maths · Differential Equations
The degree of the differential equation whose solution is \(y^2=8 a(x+a)\), is
- A 2
- B 1
- C 4
- D 3
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
We have \(y^2=8 a x+8 a^2\)
Differentiating w.r.t. \(\mathrm{x}\), we get
\(
2 y \frac{d y}{d x}=8 a \quad \Rightarrow \quad a=\left(\frac{y}{4}\right) \frac{d y}{d x}
\)
Substituting value of ' \(a\) ' in eq. (1), we get
\(y^2=8\left(\frac{y}{4}\right) \frac{d y}{d x}(x)+8\left[\left(\frac{y}{4}\right)\left(\frac{d y}{d x}\right)\right]^2=\) \(2 x y \frac{d y}{d x}+\left(\frac{y^2}{2}\right)\left(\frac{d y}{d x}\right)^2 \)
\( \therefore 2 y^2=4 x y\left(\frac{d y}{d x}\right)+y^2\left(\frac{d y}{d x}\right)^2\)
Hence order \(=1\), degree \(=2\)
Differentiating w.r.t. \(\mathrm{x}\), we get
\(
2 y \frac{d y}{d x}=8 a \quad \Rightarrow \quad a=\left(\frac{y}{4}\right) \frac{d y}{d x}
\)
Substituting value of ' \(a\) ' in eq. (1), we get
\(y^2=8\left(\frac{y}{4}\right) \frac{d y}{d x}(x)+8\left[\left(\frac{y}{4}\right)\left(\frac{d y}{d x}\right)\right]^2=\) \(2 x y \frac{d y}{d x}+\left(\frac{y^2}{2}\right)\left(\frac{d y}{d x}\right)^2 \)
\( \therefore 2 y^2=4 x y\left(\frac{d y}{d x}\right)+y^2\left(\frac{d y}{d x}\right)^2\)
Hence order \(=1\), degree \(=2\)
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 statement pattern \(\mathrm{p} \wedge(\mathrm{q} \vee \sim \mathrm{p})\) is equivalent toMHT CET 2020 Easy
- \(\tan \left\{\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right\}\) has the valueMHT CET 2022 Easy
- The sides of a triangle are \(\sin \theta, \cos \theta\) and \(\sqrt{1+\sin \theta \cos \theta}\) for some \(0 \lt \theta \lt \frac{\pi}{2}\), then the greatest angle of a triangle isMHT CET 2024 Medium
- If the p.m.f. of a discrete random variable \(X\) is \(P(X=x)=\frac{c}{x^3}\), \(x=1,2,3=0\), otherwise then \(E(X)\) is equal toMHT CET 2022 Medium
- If \(A=\left[\begin{array}{rrr}1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4\end{array}\right]\) then \(A(I+\operatorname{adj} A)=\)MHT CET 2025 Medium
- If \(\mathrm{A}=\{x, y, z\}, \mathrm{B}=\{1,2\}\), then the total number of relations from set \(\mathrm{A}\) to set \(\mathrm{B}\) areMHT CET 2020 Easy
More PYQs from MHT CET
- If the foot of the perpendicular drawn from the point (0,0,0) to the plane is (4, -2, -5) then the equation of the plane is …..MHT CET 2019 Medium
- Two monochromatic beams of intensities I and 4I respectively are superposed to form a steady interference pattern. The maximum and minimum intensities in the pattern areMHT CET 2021 Easy
- Recessive gene present on non homologous part of only one X chromosome of humans will _________ .MHT CET 2023 Easy
- If \(y=\tan ^{-1}\left(\frac{\log \left(\frac{\mathrm{e}}{x^2}\right)}{\log \left(e x^2\right)}\right)+\tan ^{-1}\left(\frac{4+2 \log x}{1-8 \log x}\right)\), then \(\frac{d y}{d x}\) isMHT CET 2023 Medium
- If \(p: A\) man is happy, \(q: A\) man is rich, then the symbolic form of ' \(A\) man is neither happy nor rich' isMHT CET 2022 Easy
- According to carbinol system tert butyl alcohol is named as,MHT CET 2025 Easy