Assertion (A): The general solution of $\frac{d^2y}{dx^2} = 0$ has two arbitrary constants.
Reason (R): The number of arbitrary constants in a general solution equals the degree of the differential equation.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Integrating twice gives $y = ax + b$ , with two constants: A is true.
R is false: the number of constants equals the order. $\frac{d^2y}{dx^2} = 0$ has order 2 but degree 1.

Concept: Constants follow the order, not the degree
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsGeneral and particular solutions

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Ten questions from Differential Equations, at your own pace.

Assertion (A): The general solution of d2ydx2=0\frac{d^2y}{dx^2} = 0dx2d2y​=0 has two arbitrary constants.Reason (R): The number of arbitrary constants in a general solution equals the degree of the differential equation.

Explanation

Assertion (A): The general solution of $\frac{d^2y}{dx^2} = 0$ has two arbitrary constants.
Reason (R): The number of arbitrary constants in a general solution equals the degree of the differential equation.