CBSE Class 12th Mathematics Chapter 9 - Differential Equations Important Questions with Answers

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Find the order and the degree of the differential equation. (Delhi 2019)
x²

\frac{d^{2} y}{d x^{2}} = {1 + {(\frac{d y}{d x})}^{2}}^{4}

Question 2.

Write the order and degree of the differential equation. (Delhi 2019, 2013)
x³

{(\frac{d^{2} y}{d x^{2}})}^{2} + x {(\frac{d y}{d x})}^{4}

= 0

Question 3.

Find the order and degree (if defined) of the differential equation. (All India 2019)

\frac{d^{2} y}{d x^{2}} + x {(\frac{d y}{d x})}^{2} = 2 x^{2} \log (\frac{d^{2} y}{d x^{2}})

Question 4.

Find the differential equation representing the family of curves y = ae^2x + 5 constant. (All India 2019)

Question 5.

Form the differential equation representing the family of curves y = e^2x(a + bx), where ‘a’ and ‘b’ are arbitrary constants. (Delhi 2019)

Question 6.

Find the differential equation of the family of curves y = Ae^2x + Be^-2x, where A and B are arbitrary constants. (All India 2019)

Question 7.

Find the general solution of the differential equation

\frac{d y}{d x}

= e^x+y. (All India 2019)

Question 8.

Solve the differential equation
(x + 1)

\frac{d y}{d x}

= 2e^-y – 1; y(0) = 0 (Delhi 2019)

Question 9.

Solve the following differential equation. x dy – y dx =

\sqrt{x^{2} + y^{2}}

dx, given that y = 0 when x = 1. (Delhi 2019; All India 2011)

Question 10.

Solve the differential equation
(1 + x)² + 2xy – 4x² = 0, subject to the initial condition y(0) = 0. (Delhi 2019)

Question 1.

Solve the differential equation

\frac{d y}{d x} - \frac{2 x y}{1 + x^{2}}

y = 1 + x² (Delhi 2019)

Question 2.

Solve the following differential equation.
x

\frac{d y}{d x}

= y – x tan

(\frac{y}{x})

. (All IndIa 2019)

Question 3.

Solve the differential equation. (All India 2019)

\frac{d y}{d x} = - [\frac{x + y \cos x}{1 + \sin x}]

Question 4.

Find the differential equation representing the family of curves y = ae^bx+5, where a and b are arbitrary constants, (CBSE 2018)

Question 5.

Solve the differential equation
cos

(\frac{d y}{d x})

= a,(a ? R) (CBSE 2018 C)

Question 6.

Find the particular solution of the differential equation e^x tany dx + (2 – e^x) sec² y dy = 0, given that y =

\frac{π}{4}

when x = 0. (CBSE 2018)

Question 7.

Find the particular solution of the differential equation

\frac{d y}{d x}

+ 2y tan x = sin x dx given that y = 0, when x =

\frac{π}{3}

(CBSE 2018; Foreign 2014)

Question 8.

Solve the differential equation (x² – y²) dx + 2xydy = 0. (CBSE 2018 C)

Question 9.

Show that the family of curves for which

\frac{d y}{d x} = \frac{x^{2} + y^{2}}{2 x y}

is given by x² – y² = cx. (Delhi 2017)

Question 10.

Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x³ – 3xy²)dx = (y³ – 3x²y)dy, where c is a parameter. (Delhi 2017)