krit.club logo

Differential Equations

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Definition, order and degree, general and particular solutions

Subtopic

Definition, order and degree, general and particular solutions under Differential Equations for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The order of the differential equation y=c1+c2exy = c_1 + c_2 e^x is:

    A.

    1

    B.

    2

    C.

    0

    D.

    3

  2. 2.

    The degree of the differential equation d2ydx2=log⁡x\frac{d^2y}{dx^2} = \log x is:

    A.

    1

    B.

    2

    C.

    Not defined

    D.

    0

  3. 3.

    The order of the differential equation representing y=Aex+Be−x+Cy = A e^x + B e^{-x} + C is:

    A.

    1

    B.

    2

    C.

    3

    D.

    0

Download the worksheet for Differential Equations - Definition, order and degree, general and particular solutions to practice offline. It includes additional chapter-level practice questions.

Solution by method of separation of variables

Subtopic

Solution by method of separation of variables under Differential Equations for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the general solution of dydx=1x+3\frac{dy}{dx} = \frac{1}{x+3}.

    A.

    y=ln⁡∣x+3∣+Cy = \ln|x+3| + C

    B.

    y=(x+3)2+Cy = (x+3)^2 + C

    C.

    y=ex+3+Cy = e^{x+3} + C

    D.

    y=1(x+3)2+Cy = \frac{1}{(x+3)^2} + C

  2. 2.

    Solve dydx=3x2y\frac{dy}{dx} = 3x^2 y.

    A.

    y=Cex3y = Ce^{x^3}

    B.

    y=x3+Cy = x^3 + C

    C.

    y=Ce3x2y = Ce^{3x^2}

    D.

    ln⁡y=3x3+C\ln y = 3x^3 + C

  3. 3.

    The solution of the differential equation dydx=12y\frac{dy}{dx} = \frac{1}{2y} is:

    A.

    y2=x+Cy^2 = x + C

    B.

    y=x+Cy = x + C

    C.

    y2=2x+Cy^2 = 2x + C

    D.

    2y2=x+C2y^2 = x + C

Download the worksheet for Differential Equations - Solution by method of separation of variables to practice offline. It includes additional chapter-level practice questions.

Solution of homogeneous differential equations of first order and first degree

Subtopic

Solution of homogeneous differential equations of first order and first degree under Differential Equations for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the degree of the function f(x,y)=x+yx2+y2f(x, y) = \frac{x+y}{x^2+y^2}?

    A.

    1

    B.

    0

    C.

    −1-1

    D.

    2

  2. 2.

    Which of these is a homogeneous differential equation of first degree (degree 1 for M,NM, N)?

    A.

    (x+y)dx+xdy=0(x+y)dx + x dy = 0

    B.

    x2dx+ydy=0x^2 dx + y dy = 0

    C.

    dx+dy=0dx + dy = 0

    D.

    ydx+(x2+y)dy=0y dx + (x^2+y) dy = 0

  3. 3.

    The function f(x,y)=x2+y2xyf(x, y) = \frac{x^2+y^2}{xy} is homogeneous of degree:

    A.

    2

    B.

    1

    C.

    0

    D.

    −1-1

Download the worksheet for Differential Equations - Solution of homogeneous differential equations of first order and first degree to practice offline. It includes additional chapter-level practice questions.

Solution of linear differential equation of the type dy/dx + py = q and dx/dy + px = q

Subtopic

Solution of linear differential equation of the type dy/dx + py = q and dx/dy + px = q under Differential Equations for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The integrating factor for dxdy+xsec⁡2y=1\frac{dx}{dy} + x \sec^2 y = 1 is:

    A.

    etan⁡ye^{\tan y}

    B.

    tan⁡y\tan y

    C.

    esec⁡ye^{\sec y}

    D.

    sec⁡2y\sec^2 y

  2. 2.

    The integrating factor of dydx+y(2xln⁡2)=1\frac{dy}{dx} + y (2^x \ln 2) = 1 is:

    A.

    2x2^x

    B.

    e2xe^{2^x}

    C.

    ln⁡2\ln 2

    D.

    exe^x

  3. 3.

    Find the integrating factor for dydx+yx=1\frac{dy}{dx} + \frac{y}{\sqrt{x}} = 1.

    A.

    exe^{\sqrt{x}}

    B.

    e2xe^{2\sqrt{x}}

    C.

    x\sqrt{x}

    D.

    2x2\sqrt{x}

Download the worksheet for Differential Equations - Solution of linear differential equation of the type dy/dx + py = q and dx/dy + px = q to practice offline. It includes additional chapter-level practice questions.

Differential Equations - Class 12 Maths (CBSE) | Krit.club