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Free CBSE - Class 12 Mathematics - Differential Equations worksheets

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1.
State True or False: Differential equation representing the family of curves $y = e^x (A\cos x + B\sin x)$ is $\frac{d^2y}{dx^2} – 2\frac{dy}{dx} + 2y = 0$.
2.
State True or False: The solution of the differential equation $\frac{dy}{dx} = \frac{x+2y}{x}$ is $x + y = kx^2$.
3.
State True or False: Solution of $\frac{dy}{dx} = \frac{y}{x} + \tan(\frac{y}{x})$ is $\sin(\frac{y}{x}) = cx$.
4.
State True or False: The differential equation of all non horizontal lines in a plane is $\frac{d^2x}{dy^2} = 0$.
5.
State True or False: Solution of the differential equation of the type $\frac{dx}{dy} + p_1 x = Q_1$ is given by $x \cdot I.F. = \int (Q_1 \times I.F.) dy$.
6.
State True or False: Correct substitution for the solution of the differential equation of the type $\frac{dy}{dx} = f(x, y)$, where $f (x, y)$ is a homogeneous function of zero degree is $y = vx$.
7.
State True or False: Correct substitution for the solution of the differential equation of the type $\frac{dx}{dy} = g(x, y)$ where $g(x, y)$ is a homogeneous function of the degree zero is $x = vy$.
8.
State True or False: Number of arbitrary constants in the particular solution of a differential equation of order two is two.
9.
State True or False: The differential equation representing the family of circles $x^2 + (y – a)^2 = a^2$ will be of order two.
10.
State True or False: The solution of $\frac{dy}{dx} = (\frac{y}{x})^{\frac{1}{3}}$ is $y^{\frac{2}{3}} – x^{\frac{2}{3}} = c$.
- OR -

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