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Differential Equations Ncert Solutions Maths class 12th Maths Class 12th Differential Equations

96. For each of the differential equations given below, indicate its order and degree (if defined):

$\begin{array}{l} (i) \frac{d^{2} y}{d x^{2}} + 5 x {(\frac{d y}{d x})}^{2} - 6 y = l o g x \\ (i i) {(\frac{d y}{d x})}^{3} - 4 {(\frac{d y}{d x})}^{2} + 7 y = s i n x \\ (i i i) \frac{d^{4} y}{d x^{4}} - s i n \frac{d^{3} y}{d x^{3}} = 0 \end{array}$

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Vishal Baghel | Contributor-Level 10

4 months ago

(i) Given: Differential equation $\frac{d^{2} y}{d x^{2}} + 5 x {(\frac{d y}{d x})}^{2} - 6 y = l o g x$

The highest order derivative present in this differential equation is $\frac{d^{2} y}{d x^{2}}$ and hence order of this differential equation if 2.

The given differential equation is a polynomial equation in derivatives and highest power of the highest order derivative $\frac{d^{2} y}{d x^{2}}$ is 1.

Therefore, Order = 2, Degree = 1

(ii) Given: Differential equation ${(\frac{d y}{d x})}^{3} - 4 {(\frac{d y}{d x})}^{2} + 7 y = s i n x$

The highest order derivative present in this differential equation is $\frac{d y}{d x}$ and hence order of this differential equation if 1.

The given differential equation is a polynomial equation in derivatives and highest power of the highest order derivativ

...more

(i) Given: Differential equation $\frac{d^{2} y}{d x^{2}} + 5 x {(\frac{d y}{d x})}^{2} - 6 y = l o g x$

The highest order derivative present in this differential equation is $\frac{d^{2} y}{d x^{2}}$ and hence order of this differential equation if 2.

The given differential equation is a polynomial equation in derivatives and highest power of the highest order derivative $\frac{d^{2} y}{d x^{2}}$ is 1.

Therefore, Order = 2, Degree = 1

(ii) Given: Differential equation ${(\frac{d y}{d x})}^{3} - 4 {(\frac{d y}{d x})}^{2} + 7 y = s i n x$

The highest order derivative present in this differential equation is $\frac{d y}{d x}$ and hence order of this differential equation if 1.

The given differential equation is a polynomial equation in derivatives and highest power of the highest order derivative $\frac{d y}{d x}$ is 3.

Therefore, Order = 1, Degree = 3

(iii) Given: Differential equation $\frac{d^{4} y}{d x^{4}} - s i n \frac{d^{3} y}{d x^{3}} = 0$

The highest order derivative present in this differential equation is $\frac{d^{4} y}{d x^{4}}$ and hence order of this differential equation if 4.

The given differential equation is not a polynomial equation in derivatives therefore, degree of this differential equation is not defined.

Therefore, Order = 4, Degree not defined

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96. For each of the differential equations given below, indicate its order and degree (if defined): (i)d2ydx2+5x(dydx)2−6y=logx(ii)(dydx)3−4(dydx)2+7y=sinx(iii)d4ydx4−sind3ydx3=0

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