Question:
The order and degree of the differential equation \(\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}\) are \(\ldots\)
The order and degree of the differential equation \(\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}\) are \(\ldots\)
Show Hint
Remove the radicals and fractions so that all derivatives appear as polynomials, then read off the order and degree.
Updated On: Oct 1, 2026
- Order 2, Degree 3
- Order 2, Degree 2
- Order 3, Degree 3
- Order 3, Degree 2
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
The order is the highest derivative present. The degree is the power of the highest order derivative after the equation has been made a polynomial in the derivatives.
Step 2: Key Formula or Approach:
Square both sides to remove the outer square root, then clear the fraction.
Step 3: Detailed Explanation:
Given
\[ \sqrt{1 + \frac{1}{(y')^2}} = (y'')^{3/2} \]
Square both sides:
\[ 1 + \frac{1}{(y')^2} = (y'')^3 \]
Multiply through by \((y')^2\):
\[ (y')^2 + 1 = (y')^2\,(y'')^3 \]
Now every derivative has an integer power. The highest derivative is \(y''\), so the order is 2. Its power is 3, so the degree is 3.
Order 2 with degree 2 in option (B) and the order 3 options (C) and (D) do not match: there is no third derivative anywhere.
Final Answer:
The order is 2 and the degree is 3, option (A). \[ \boxed{\text{Order 2, Degree 3 (A)}} \]
The order is the highest derivative present. The degree is the power of the highest order derivative after the equation has been made a polynomial in the derivatives.
Step 2: Key Formula or Approach:
Square both sides to remove the outer square root, then clear the fraction.
Step 3: Detailed Explanation:
Given
\[ \sqrt{1 + \frac{1}{(y')^2}} = (y'')^{3/2} \]
Square both sides:
\[ 1 + \frac{1}{(y')^2} = (y'')^3 \]
Multiply through by \((y')^2\):
\[ (y')^2 + 1 = (y')^2\,(y'')^3 \]
Now every derivative has an integer power. The highest derivative is \(y''\), so the order is 2. Its power is 3, so the degree is 3.
Order 2 with degree 2 in option (B) and the order 3 options (C) and (D) do not match: there is no third derivative anywhere.
Final Answer:
The order is 2 and the degree is 3, option (A). \[ \boxed{\text{Order 2, Degree 3 (A)}} \]
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Order and Degree of Differential Equation Questions
- What is the order of the differential equation \( \dfrac{d^2 y}{dx^2} + \left(\dfrac{dy}{dx}\right)^3 = 0 \)?
- The differential equation of $y = e^x (a \cos x + b \sin x)$ is
- The differential equation representing the family of curves $y^2 = 2c(x + \sqrt{c})$, where $c$ is a positive parameter, is of}
- The degree of the differential equation \(\frac{d^2y}{dx^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log \left( \frac{d^2y}{dx^2} \right)\) is
- The differential equation of family of circles whose centres lie on X-axis is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions