Q21Written answer
Solve the differential equation dy = cos x (2 – y cosec x) dx given that y = 2 when x = π/2.
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Worked solution
Given differential equation, dy = cos x (2 – y cosec x) dx
NCERT Exemplar · Class 12 · Maths
Chapter 9: Differential Equations
Practice each question, then open the answer or worked solution.
Questions
38 questionsQ22Written answer
Form the differential equation by eliminating A and B in Ax2 + By2 = 1.
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Worked solution
Given, Ax2 + By2 = 1
Differentiating w.r.t. x, we get
Q23Written answer
Solve the differential equation (1 + y2) tan–1x dx + 2y (1 + x2) dy = 0.
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Worked solution
Given differential equation, (1 + y2) tan–1x dx + 2y (1 + x2) dy = 0
2y (1 + x2) dy = -(1 + y2) tan-1x dx
Thus, the above equation is the required solution.
Q24Written answer
Find the differential equation of system of concentric circles with centre (1, 2).
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Worked solution
The family of concentric circles with centre (1, 2) and radius ‘r’ is given by
(x – 1)2 + (y – 2)2 = r2
Differentiating both sides w.r.t, x we get
Thus, the above is the required equation.
Long Answer (L.A.)
Q25Written answer
Solve :
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Worked solution
Given differential equation,
Q26Written answer
Find the general solution of (1 + tan y) (dx – dy) + 2xdy = 0.
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Worked solution
Given, (1 + tan y) (dx – dy) + 2xdy = 0
Q27Written answer
Solve: dy/dx = cos(x + y) + sin (x + y). [Hint: Substitute x + y = z]
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Worked solution
Q28Written answer
Find the general solution of dy/dx – 3y = sin 2x.
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Worked solution
Given equation, dy/dx – 3y = sin 2x
It’s a first order linear differential equation
Here P = -3 and Q = sin 2x
Q29Written answer
Find the equation of a curve passing through (2, 1) if the slope of the tangent to the curve at any point (x, y) is (x2 + y2)/ 2xy.
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Worked solution
Given that the slope of tangent to a curve at (x, y) is (x2 + y2)/ 2xy.
It’s a homogeneous differential function
Q30Written answer
Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve at any point (x, y) is (y – 1)/ (x2 + x)
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Worked solution
Given that the slope of the tangent to the curve at (x, y) is
As, the line is passing through the point (1, 0), then (0 – 1) (1 + 1) = c(1) ⇒ c = 2
Thus, the required solution is (y – 1) (x + 1) = 2x.