KCET · Maths · Differential Equations
The order of the differential equation \( y=c_{1} e^{c_{2}+x}+c_{3} e^{c_{4}+x} \) is
- A \( 02 \)
- B \( 04 \)
- C \( 1 \)
- D \( 13 \)
Answer & Solution
Correct Answer
(C) \( 1 \)
Step-by-step Solution
Detailed explanation
\( (\mathrm{C}) \)
\[
\begin{array}{l}
y=c_{1} e^{c_{2}+x}+c_{3} e^{c_{4}+x} \\
=\left(c_{1} e^{c_{2}}+c_{3} e^{c_{4}}\right) e^{x} \\
=A e^{x} \\
\frac{d y}{d x}-A e^{x}=y \\
\Rightarrow \text { order }=1
\end{array}
\]
\[
\begin{array}{l}
y=c_{1} e^{c_{2}+x}+c_{3} e^{c_{4}+x} \\
=\left(c_{1} e^{c_{2}}+c_{3} e^{c_{4}}\right) e^{x} \\
=A e^{x} \\
\frac{d y}{d x}-A e^{x}=y \\
\Rightarrow \text { order }=1
\end{array}
\]
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
\(f(x)=\left\{\begin{array}{cl}\frac{\left.x^{2}-(a+2) x+a\right)}{x-2} & x \neq 2 \\ 2 & , x=2\end{array} \quad\right.\) is continuous at \(x=2\), then the value of \(a\) isKCET 2012 Easy - The remainder when, \(10^{10} \cdot\left(10^{10}+1\right)\left(10^{10}+2\right)\) is divided by 6 isKCET 2013 Medium
- The simplified form of \( \tan ^{-1}\left(\frac{x}{y}\right)-\tan ^{-1}\left(\frac{x-y}{x+y}\right) \) is equal toKCET 2016 Medium
- \(\sum\limits_{n=1}^{4} (-1)^{2n} \cdot i^{2n} = \)KCET 2026 Easy
- A function is \(f(x)=\left\{\begin{array}{cc}\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0\end{array}\right.\)KCET 2025 Medium
- If \(\sin 2 x=4 \cos x\), then \(x\) is equal toKCET 2012 Easy
More PYQs from KCET
- Butylated hydroxy toluene as a food additive acts asKCET 2014 Medium
- Given below are two statements:
Statement-I: The \(\text{M}-\text{C}\) \(\sigma\) bond is formed by the donation of lone pair of electrons on the carbonyl carbon into a vacant d-orbital of the metal.
Statement-II: The \(\text{M}-\text{C}\) \(\pi\) bond is formed by the donation of a pair of electrons from a filled d-orbital of metal into the vacant antibonding \(\pi^*\) orbital of carbon monoxide.
In the light of the above statements, choose the correct answer from the options given below:KCET 2026 Medium - The term "Molecular Scissors" refers toKCET 2022 Easy
- Tertiary alkyl halide is practically to substitution by \( S_{N} 2 \) mechanism because ofKCET 2018 Easy
- The quantity of a charge that will be transferred by a current flow of \( 20 \) A over \( 1 \) hour \( 30 \)
minutes period isKCET 2016 Easy - A balloon which always remains spherical is being inflated by pumping in \( 10 \) cubic centimeters
of gas per second. Find the rate at which the radius of the balloon is increasing when the
radius is \( 15 \mathrm{cms} \).KCET 2015 Medium