AP EAMCET · Maths · Differential Equations
The integrating factor of the linear directional equation \(\frac{d y}{d x}+P(x) y=Q(x)\) is a solution of the differential equation
- A \(\frac{d y}{d x}-P(x) y=0\)
- B \(\frac{d y}{d x}+P(x) y=0\)
- C \(\frac{d y}{d x}-\frac{y}{x}=P(x)\)
- D \(\frac{d y}{d x}+\frac{x}{y}=P(x)\)
Answer & Solution
Correct Answer
(A) \(\frac{d y}{d x}-P(x) y=0\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}+P(x) y=Q(x)\) \(\begin{aligned} & \text { Integrating }=e^{\int P(x) d x} \\ & \text { Factor }\end{aligned}\) (A) If \(y=e^{\int p(x) d x}\) checking: \(\frac{d y}{d x}-P(x) y=0\) \(\frac{d y}{d x}=e^{\int {p}(x) d x}\) \(P(x)=y P(x)\)…
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 \(f: R \rightarrow A\) defined by \(f(x)=\frac{1}{x^2+2 x+2}\), \(\forall x \in R\) is surjective, then \(A=\)AP EAMCET 2018 Medium
- If \(l_1\) and \(l_2\) are the lengths of the perpendiculars drawn from a point on the hyperbola \(5 x^2-4 y^2-20=0\) to its asymptotes, then \(\frac{l_1^2 l_2^2}{100}=\)AP EAMCET 2024 Easy
- \(\int_0^{3 \pi / 2} \frac{\cos ^3 x}{\cos ^3 x+\sin ^3 x} d x=\)AP EAMCET 2025 Medium
- The set of values of \(x\) for which \(f(x)=3 x^4-8 x^3-6 x^2+24 x-12\) is an increasing function, isAP EAMCET 2018 Easy
- The locus of a variable point whose chord of contact w.r.t. the hyperbola subtends a right angle at the origin isAP EAMCET 2022 Medium
- The two pairs of straight lines \(12 x^2+7 x y-12 y^2=0\) and \(12 x^2+7 x y-12 y^2-x+7 y-1=0\) constitute aAP EAMCET 2022 Medium
More PYQs from AP EAMCET
- A pungent smelling gas \(A\) gives dense white fumes with conc. \(\mathrm{HCl}\). When \(A\) reacts with alkaline solution of a colourless reagent \(B\), a reddish-brown precipitate \(C\) is formed. The compounds \(A, B, C\) respectively areAP EAMCET 2020 Hard
- \(\int \frac{x^4+1}{x^6+1} d x=\)AP EAMCET 2024 Medium
- If the values of the temperature of a body in Fahrenheit and Celcius scales are in the ratio of \(13: 5\), then the temperature of the body isAP EAMCET 2025 Easy
- Find the function \(g(t)\) if \(f(t)=3 t-2\) and \((g \circ f)^{-1}(t)=t-2\).AP EAMCET 2020 Medium
- The values of \(x\) for which \(\sin x+i \cos 2 x\) and \(\cos x-i \sin 2 x\) are conjugate to each other areAP EAMCET 2022 Easy
- A constant voltage of \(25 \mathrm{~V}\) is applied to a series \(L-R\) circuit at \(t=0\), by closing a switch. What is the potential difference across the resistor and the inductor at time \(t=0\) ?AP EAMCET 2011 Medium