Exams › JEE Main › Maths
Solve the differential equation d³y/dx³ - 6 d²y/dx² + 11 dy/dx - 6y = 0.
- y = (c1 + c2*x + c3*x²)e^x
- y = x(c1*e^x + c2*e^(2x) + c3*e^(3x))
- y = c1*e^x + c2*e^(2x) + c3*e^(3x)
- none of these
Correct answer: y = c1*e^x + c2*e^(2x) + c3*e^(3x)
Solution
The characteristic equation has distinct roots m = 1, 2, 3, so the general solution is a combination of e^x, e^(2x), e^(3x).
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 →