The number of arbitrary constants in the general solution y d2 y-d x2-d y-d x2-sin x is

We saw that general solution of a differential equation will have as many arbitrary constants as the nbsp; order of the differential equation. Order of the di ...

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Standard XII

Mathematics

Order of a Differential Equation

The number of...

Question

The number of arbitrary constants in the general solution of $y \frac{d^{2} y}{d x^{2}} + (\frac{d y}{d x})^{2} = sin x$ is ___

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Solution

We saw that general solution of a differential equation will have as many arbitrary constants as the order of the differential equation. Order of the differential equation $y \frac{d^{2} y}{d x^{2}} + (\frac{d y}{d x})^{2} = sin x$ is 2, becuase $\frac{d^{2} y}{d x^{2}}$ is the highest differential appearing in the equation.
So the number of arbitrary constants = order = 2

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The number of arbitrary constants in the general solution of yd2ydx2+(dydx)2=sinx is ___

The number of arbitrary constants in the general solution of $y \frac{d^{2} y}{d x^{2}} + (\frac{d y}{d x})^{2} = sin x$ is ___