Differential Equations

Class 12 · Mathematics · 96 Questions

1beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

d4ydx4+sin⁡(y′′)=0\frac{d^4y}{dx^4} + \sin(y'') = 0
2beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

y′+5y=0y' + 5y = 0
3beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

(dsdt)4+3sd2sdt2=0\left(\frac{ds}{dt}\right)^4 + 3s \frac{d^2s}{dt^2} = 0
4beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

(d2ydx2)2+cos⁡(dydx)=0\left(\frac{d^2y}{dx^2}\right)^2 + \cos\left(\frac{dy}{dx}\right) = 0
5beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

d2ydx2=cos⁡3x+sin⁡3x\frac{d^2y}{dx^2} = \cos 3x + \sin 3x
6beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

(y′′)2+(y′′)3+(y′)4+y5=0(y'')^2 + (y'')^3 + (y')^4 + y^5 = 0
7beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

y′′+2y′′+y′=0y'' + 2y'' + y' = 0
8beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

y′+y=exy' + y = e^x
9beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

y′′+(y′)2+2y=0y'' + (y')^2 + 2y = 0
10beginner💡 Understand1 markVery Short

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

y′′+2y′+sin⁡y=0y'' + 2y' + \sin y = 0
11beginner💡 Understand1 markMCQ

The degree of the differential equation

(d2ydx2)3+(dydx)2+sin⁡(dydx)+1=0\left(\frac{d^2 y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^2 + \sin \left(\frac{dy}{dx}\right) + 1 = 0
12beginner💡 Understand1 markMCQ

The order of the differential equation

2x2d2ydx2−3dydx+y=02x^2 \frac{d^2 y}{dx^2} - 3 \frac{dy}{dx} + y = 0
1beginner🔧 Apply2 marksShort Answer

In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=ex+1y = e^x + 1 : y′′−y′=0y'' - y' = 0

2beginner🔧 Apply2 marksShort Answer

In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=x2+2x+Cy = x^2 + 2x + C : y′−2x−2=0y' - 2x - 2 = 0

3beginner🔧 Apply2 marksShort Answer

In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=cos⁡x+Cy = \cos x + C : y′+sin⁡x=0y' + \sin x = 0

4beginner🔧 Apply2 marksShort Answer

In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=1+x2y = \sqrt{1+x^2} : y′=xy1+x2y' = \frac{xy}{1+x^2}

5beginner🔧 Apply2 marksShort Answer

In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=Axy = Ax : xy′=y(x≠0)xy' = y (x \neq 0)

6intermediate🔧 Apply2 marksShort Answer

In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=xsin⁡xy = x \sin x : xy′=y+xx2−y2(x≠0 and x>y or x<−y)xy' = y + x \sqrt{x^2 - y^2} (x \neq 0 \text{ and } x > y \text{ or } x < -y)

7intermediate🔧 Apply2 marksShort Answer

In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: xy=log⁡y+Cxy = \log y + C : y′=y21−xy(xy≠1)y' = \frac{y^2}{1-xy} (xy \neq 1)

8intermediate🔧 Apply2 marksShort Answer

In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y−cos⁡y=xy - \cos y = x : (ysin⁡y+cos⁡y+x)y′=y(y \sin y + \cos y + x) y' = y

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