AP EAMCET · Maths · Differential Equations
If \(c_1, c_2, c_3, c_4, c_5\) are arbitrary constants, then the order of the differential equation whose general solution is \(y=\left(c_1+c_2\right) \sin \left(x+c_3\right)+c_4 e^{x+c_5}\) is
- A 3
- B 5
- C 4
- D Not defined
Answer & Solution
Correct Answer
(A) 3
Step-by-step Solution
Detailed explanation
General solution of differential equation is, \(y=\left(C_1+C_2\right) \sin \left(x+C_3\right)+C_4 e^{x+C_5}\) Here solution is of form; \(\begin{aligned} & y=A \sin \left(x+C_3\right)+B e^x \\ & {\left[\because C_1+C_2=A, C_4 e^c=B\right] } \end{aligned}\) So, there are…
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
- In a test a student either guesses or copies or knows the answer to answer a multiple choice question with four choices. The probability that he makes a guess is \(1 / 3\) and the probability that he copies the answer is \(1 / 6\). The probability that his answer is correct, given that he copied it is \(1 / 8\). The probability that he knew the answer to the question, given that he answered it correctly isAP EAMCET 2023 Hard
- The equation of the common tangent drawn to the curves \(y^2=8 x\) and \(x y=-1\) isAP EAMCET 2016 Medium
- In the expansion of \(\frac{2 x+1}{(1+x)(1-2 x)}\), the sum of the coefficients of the first 5 odd powers of \(x\) isAP EAMCET 2024 Medium
- The perpendicular distance from the origin to the focal chord drawn through the point \((4,5)\) to the parabola \(y^2-4 y-3 x+7=0\) isAP EAMCET 2023 Medium
- The number of solutions of the equation \(\sec x \cos 5 x+1=0\) in the interval \([0,2 \pi]\) isAP EAMCET 2025 Medium
- If \((a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^2-b^2\) where \(a>b>0\), then at \(\left(\frac{\pi}{4}, \frac{\pi}{4}\right)\),
\(\frac{\mathrm{dy}}{\mathrm{dx}}=\)AP EAMCET 2025 Medium
More PYQs from AP EAMCET
- 25 capacitors each of capacitance \(1 \mu \mathrm{F}\) are connected in series to a battery of \(100 \mathrm{~V}\). The total charge stored on capacitors isAP EAMCET 2022 Easy
- Identify the set which does not have ambidentate ligand (s)AP EAMCET 2025 Medium
- The displacement of a body when it covers a distance of \(C / 4\) (where, \(C\) is circumference) along the circumference of the circle of radius \(r\) with a uniform speed \(u\) isAP EAMCET 2020 Medium
- If \(\cos (\alpha+\beta)=\frac{4}{5}, \sin (\alpha-\beta)=\frac{5}{13}\) and \(\alpha, \beta\) between 0 and \(\frac{\pi}{4}\), then \(\tan 2 \alpha\) is equal toAP EAMCET 2002 Easy
- Aluminium chloride in acidified aqueous solution gives a complex ion ' \(X^{\prime}\). The hybridisation of central atom in \(X\) isAP EAMCET 2022 Easy
- Imaginary part of \(\frac{(1-i)^3}{(2-i)(3-2 i)}\) isAP EAMCET 2024 Easy