第12类NCERT解决方案-数学第二部分–第9章微分方程-练习-9.1

确定练习1至10中给出的微分方程的阶数和阶数(如果已定义)。

问题1 $\frac{d^4y}{dx^4}+\sin(y''')=0$

解决方案：

Given: $\frac{d^4y}{dx^4}+\sin(y''')=0$

Here the order is 4 and degree is not defined because it is not a polynomial function.

问题2. y’+ 5y = 0

解决方案：

Given: y’ + 5y = 0

Here, the order is 1 and the degree is also 1.

问题3。 $(\frac{ds}{dt})^{4}+3s\frac{d^{2}s}{dt^{2}}=0$

解决方案：

Given: $(\frac{ds}{dt})^{4}+3s\frac{d^{2}s}{dt^{2}}=0$

Here, the order is 2 and the degree is 1.

问题4。 $(\frac{d^{2}y}{dx^{2}})=\cos(\frac{dy}{dx})=0$

解决方案：

Given: $(\frac{d^{2}y}{dx^{2}})=\cos(\frac{dy}{dx})=0$

Here, the order is 2 and degree is not defined because it is not a polynomial function.

问题5 $(\frac{d^{2}y}{dx^{2}})=\cos3x+\sin3x$

解决方案：

Given: $(\frac{d^{2}y}{dx^{2}})=\cos3x+\sin3x$

Here, the order is 2 and degree is 1.

问题6.(y”’) ² +(y”) ³ + y(’) ⁴ + y ⁵ = 0

解决方案：

Given: (y”’)² + (y”)³ + y(‘)⁴ + y⁵ = 0

The order is 3 and the degree is 2.

问题7。y” + 2y” + y’= 0

解决方案：

Given: y”’ + 2y” + y’ = 0

The order is 3 and the degree is 1

问题8. y’+ y = e ^x

解决方案：

Given: y’ + y = e^x

The order is 1 and the degree is 1.

问题9。y” +(y’) ² + 2y = 0

解决方案：

Given: y” + (y’)² + 2y = 0

The order is 3 the degree is 1

问题10。y” + 2y’+ sin y = 0

解决方案：

Given: y” + 2y’ + sin y = 0

The order is 2 and the degree is one.

问题11.微分方程的阶数

$(\frac{d^2y}{dx^2})^{3}+(\frac{dy}{dx})^{2}+sin(\frac{dy}{dx})+1=0$是

(A)3(B)2(C)1(D)未定义

解决方案：

Given: $(\frac{d^2y}{dx^2})^{3}+(\frac{dy}{dx})^{2}+sin(\frac{dy}{dx})+1=0$

Here, the degree is not defined.     

So, the correct option is D.

问题12.微分方程的阶数

$2x^1\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0$是

(A)3(B)2(C)1(D)未定义

解决方案：

Given: $2x^1\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0$

Here, the order is 2. 

So, the correct option is A.