AP EAMCET · Maths · Differential Equations
If the slope of the tangent drawn at any point \((x, y)\) on a curve is \((x+y)\), then the equation of that curve is
- A \(y=c e^x+1+x\)
- B \(y=c e^x-x\)
- C \(\mathrm{y}=\mathrm{ce}^{-\mathrm{x}}-1-\mathrm{x}\)
- D \(\mathrm{y}=\mathrm{ce}^{\mathrm{x}}-1-\mathrm{x}\)
Answer & Solution
Correct Answer
(D) \(\mathrm{y}=\mathrm{ce}^{\mathrm{x}}-1-\mathrm{x}\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = x+y\) \(\frac{dy}{dx} - y = x\) IF \( = e^{\int -1 dx} = e^{-x}\) \(y \cdot e^{-x} = \int x e^{-x} dx\) \(y e^{-x} = -x e^{-x} - e^{-x} + C\) \(y = C e^x - x - 1\)
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
- Let \(a, b\) and \(c\) be unit vectors such that \(a\) is perpendicular to the plane containing \(\mathbf{b}\) and \(\mathbf{c}\) and angle between \(\mathbf{b}\) and \(\mathbf{c}\) is \(\frac{\pi}{3}\). Then,\(|\mathbf{a}+\mathbf{b}+\mathbf{c}|=\)AP EAMCET 2022 Medium
- In \(\triangle A B C\), if \((a-b)(s-c)=(b-c)(s-a)\), then \(r_1, r_2, r_3\) are inAP EAMCET 2023 Medium
- \(\lim _{x \rightarrow 0} \frac{6^x-3^x-2^x+1}{x^2}\) is equal toAP EAMCET 2016 Easy
- In a triangle \(A B C\), if \(\left(r_1-r_3\right)\left(r_1-r_2\right)-2 r_2 r_3=0\), then \(a^2-b^2=\)AP EAMCET 2025 Medium
- If \(|x| < 1\), then the coefficient of \(x^5\) in the expansion of \(\frac{3 x}{(x-2)(x+1)}\) isAP EAMCET 2015 Medium
- If \(\sin \theta+\cos \theta=p\) and \(\tan \theta+\cot \theta=q\), then \(q\left(p^2-1\right)\) is equal toAP EAMCET 2015 Easy
More PYQs from AP EAMCET
- If \(y=\sqrt{3} x+k_1\) and \(y=\sqrt{3} x+k_2\) are two parallel tangents of a circle of radius 2 units, then \(\left|k_1-k_2\right|\) is equal toAP EAMCET 2020 Medium
- The mid-point of the line segment joining the centroid and the orthocentre of the triangle whose vertices are \((a, b),(a, c)\) and \((d, c)\), isAP EAMCET 2016 Easy
- The range of the function \(f(x)=\frac{x}{x^2-5 x+9}\) isAP EAMCET 2022 Easy
- The time period of revolution of a satellite close to planet's surface is 80 minutes. The time period of another satellite which is at a height of 3 times the radius of the planet from surface isAP EAMCET 2024 Easy
- The distance between the tangent lines to the hyperbola \(x^2-2 y^2=18\) which are perpendicular to the line \(y=x\) isAP EAMCET 2022 Medium
- 117.An L-C resonant circuit contains a 400 pF capacitor and an inductor of 400 μH. It is coupled to an antenna. Wavelength of
radiated electromagnetic wave isAP EAMCET 2021 Medium