Question:
The degrees of the differential equations $\frac{dy}{dx}+y^{2} = x$ and $\frac{d^{2}y}{dx^{2}} + y = sin\,x$ are equal.
The degree of a differential equation, when it is a polynomial equation in derivatives, is the highest positive integral power of the highest order derivative involved in the differential equation, otherwise degree is not defined.
The degrees of the differential equations $\frac{dy}{dx}+y^{2} = x$ and $\frac{d^{2}y}{dx^{2}} + y = sin\,x$ are equal.
The degree of a differential equation, when it is a polynomial equation in derivatives, is the highest positive integral power of the highest order derivative involved in the differential equation, otherwise degree is not defined.
Updated On: Jul 28, 2022
- Statement 1 is true, Statement 2 is true. Statement 2 is not a correct explanation of Statement 1.
- Statement 1 is felse, Statement 2 is true.
- Statement 1 is true, Statement 2 is false.
- Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
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The Correct Option is D
Solution and Explanation
Given differential equations are
$\frac{dy}{dx}+y^{2} = x$ and $\frac{d^{2}y}{dx^{2}} + y = sin\,x $
Their degrees are 1.
Both have equal degree.
Also, Statement - 2 is the correct explanation for Statement -1.
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Concepts Used:
Order and Degree of Differential Equation
The equation that helps us to identify the type and complexity of the differential equation is the order and degree of a differential equation.
The Order of a Differential Equation:
The highest order of the derivative that appears in the differential equation is the order of a differential equation.
The Degree of a Differential Equation:
The highest power of the highest order derivative that appears in a differential equation is the degree of a differential equation. Its degree is always a positive integer.
For examples:
- 7(d4y/dx4)3 + 5(d2y/dx2)4+ 9(dy/dx)8 + 11 = 0 (Degree - 3)
- (dy/dx)2 + (dy/dx) - Cos3x = 0 (Degree - 2)
- (d2y/dx2) + x(dy/dx)3 = 0 (Degree - 1)