What is the degree of the following differential equation- 5 x d y d x 2-d 2 y d x 2-6 y-log x

5xdydx2 d2ydx2 6y=log #160;x Here, we see that nbsp; the highest order derivative is d2ydx2 and its power is 1. Therefore, the given differential equation i ...

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Standard XII

Mathematics

Order of a Differential Equation

What is the d...

Question

What is the degree of the following differential equation?
$5 x {(\frac{d y}{d x})}^{2} - \frac{d^{2} y}{d x^{2}} - 6 y = \log x$

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Solution

$5 x {(\frac{d y}{d x})}^{2} - \frac{d^{2} y}{d x^{2}} - 6 y = \log x$
Here, we see that the highest order derivative is $\frac{d^{2} y}{d x^{2}}$ and its power is 1.
Therefore, the given differential equation is of first degree.

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Similar questions

Q. Write the degree of the differential equation

\frac{d^{2} y}{d x^{2}} + x {(\frac{d y}{d x})}^{2} = 2 x^{2} \log (\frac{d^{2} y}{d x^{2}})

Q. Find the sum of the order and degree of the differential equation

y = x {(\frac{d y}{d x})}^{3} + \frac{d^{2} y}{d x^{2}}

Q. Verify that the function y = e^−3x is a solution of the differential equation

\frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} - 6 y = 0

Q. For each of the differential equation given below, indicate its order and degree (if defined).
(i)

\frac{d^{2} y}{d x^{2}} + 5 x {(\frac{d y}{d x})}^{2} - 6 y = log x

(ii)

{(\frac{d y}{d x})}^{3} - 4 {(\frac{d y}{d x})}^{2} + 7 y = sin x

(iii)

\frac{d^{4} y}{d x^{4}} - sin (\frac{d^{3} y}{d x^{3}}) = 0

Q. Which of the following differential equations has y = C₁ e^x + C₂ e⁻^x as the general solution?
(a)

\frac{d^{2} y}{d x^{2}} + y = 0

(b)

\frac{d^{2} y}{d x^{2}} - y = 0

(c)

\frac{d^{2} y}{d x^{2}} + 1 = 0

(d)

\frac{d^{2} y}{d x^{2}} - 1 = 0

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What is the degree of the following differential equation? 5xdydx2-d2ydx2-6y=log x

5xdydx2-d2ydx2-6y=log x Here, we see that the highest order derivative is d2ydx2 and its power is 1. Therefore, the given differential equation is of first degree.

What is the degree of the following differential equation?
$5 x {(\frac{d y}{d x})}^{2} - \frac{d^{2} y}{d x^{2}} - 6 y = \log x$

$5 x {(\frac{d y}{d x})}^{2} - \frac{d^{2} y}{d x^{2}} - 6 y = \log x$
Here, we see that the highest order derivative is $\frac{d^{2} y}{d x^{2}}$ and its power is 1.
Therefore, the given differential equation is of first degree.