Home › UP Board Class 12 › mathematics › Differential Equations › The general solution of a 3rd-order DE contains …
The general solution of a 3rd-order DE contains how many arbitrary constants?
AOne arbitrary constant
BTwo arbitrary constants
CThree arbitrary constants
DSix arbitrary constants
Answer & Solution
Correct answer: C. Three arbitrary constants
Number of arbitrary constants in general solution = order of the DE. For 3rd-order, 3 constants. Particular solution fixes them via 3 initial conditions.
Related questions
Solution of dy/dx = ky (k > 0) representsThe degree of (d²y/dx²)² + (dy/dx)³ + y = 0 isThe order of the differential equation d²y/dx² + 3 dy/dx + 2y = 0 isEuler's method for a DE y' = f(x, y) computes the next value as:A mass on a spring obeys d²x/dt² + ω²x = 0 (SHM). The period of oscillation is:For the second-order LDE y'' − 5y' + 6y = 0, the auxiliary equation m² − 5m + 6 = 0 has roBy Newton's law of cooling, a hot tea cup at 90°C in a room at 25°C cools so that:If a population grows exponentially as dN/dt = 0.1 N (with t in years), the DOUBLING TIME