Exams › JEE Main › Maths
Find the implicit solution of the differential equation cos y (dy)/(dx)=e^(x+sin y)+x²e^(sin y).
- e^x-e^(-sin y)+(x³)/(3)=C
- e^(-x)-e^(-sin y)+(x³)/(3)=C
- e^x+e^(-sin y)+(x³)/(3)=C
- e^x-e^(sin y)-(x³)/(3)=C
Correct answer: e^x+e^(-sin y)+(x³)/(3)=C
Solution
Factor RHS as e^(siny)(e^x+x^2), giving cosy*e^(-siny) dy = (e^x+x^2) dx. Integrating: -e^(-siny) = e^x + x^3/3 + const, i.e. e^x + e^(-siny) + x^3/3 = C.
Related JEE Main Maths questions
- If √(1-x²ⁿ)+√(1-y²ⁿ)=a(xⁿ-yⁿ), then the value of (√(1-x²ⁿ) dy)/(√(1-y²ⁿ) dx) is
- For a curve that passes through the point (4, 0), the slope is governed by
dy/dx = y/x + 5x/((x + 2)(x − 3)).
If the point (5, a) lies on this curve, what is the value of a?
- Which differential equation represents the family of all conics whose axes are aligned with the coordinate axes?
- Find the equation of the curve that satisfies (xy - x²) (dy)/(dx) = y² and passes through the point (-1, 1).
- For the differential equation y = y/x + x/y, if its general solution is written as y = x / log|Cx|, then the function φ(x/y) is
- For the differential equation dy/dx = [y f'(x) − y²]/f(x), where f(x) is a specified function, the solution is
⚔️ Practice JEE Main Maths free + battle 1v1 →