Question:
The elimination of arbitrary constants $c_{1}, c_{2}, c_{3}, c_{4}$ from $y=(c_{1}+c_{2})\sin(2x+c_{3}) + c_{4}e^{5x}$ gives a differential equation of order ________.
The elimination of arbitrary constants $c_{1}, c_{2}, c_{3}, c_{4}$ from $y=(c_{1}+c_{2})\sin(2x+c_{3}) + c_{4}e^{5x}$ gives a differential equation of order ________.
Show Hint
Combine dependent constants (like $c_1+c_2$) before counting.
Updated On: Jun 26, 2026
- 2
- 4
- 3
- 1
- 5
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Concept
The order of the differential equation equals the number of independent arbitrary constants.
Step 2: Meaning
Identify independent constants. $(c_1 + c_2)$ is a single constant (say $K$).
Step 3: Analysis
The equation is $y = K\sin(2x + c_3) + c_4e^{5x}$. The constants are $K, c_3,$ and $c_4$.
Step 4: Conclusion
There are 3 independent constants, so the order is 3. Final Answer: (C)
The order of the differential equation equals the number of independent arbitrary constants.
Step 2: Meaning
Identify independent constants. $(c_1 + c_2)$ is a single constant (say $K$).
Step 3: Analysis
The equation is $y = K\sin(2x + c_3) + c_4e^{5x}$. The constants are $K, c_3,$ and $c_4$.
Step 4: Conclusion
There are 3 independent constants, so the order is 3. Final Answer: (C)
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Order and Degree of Differential Equation Questions
- The order and the degree of the differential equation $2\frac{dy}{dx}-3x=\left(2y-x\frac{dy}{dx}\right)^{-3}$ respectively, are
- The number of solutions of \( \frac{dy}{dx} = y^{1/3} \) passing through origin is
The degree of the differential equation
\[ \left[1 + \left(\frac{dy}{dx}\right)^2 \right]^{3/2} = \frac{d^2 y}{dx^2} \]
is ______.
- The order and degree of the differential equation $\frac{d^{2}y}{dx^{2}}+\sqrt{x^{2}+\left(\frac{dy}{dx}\right)^{3/2}}=0$ are respectively
- The order and degree of the differential equation \( (y'')^2 + (y''')^3 - (y')^4 + y^5 = 0 \) is
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions