Q11Written answer
If y(x) is a solution of and y (0) = 1, then find the value of y(π/2).
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NCERT Exemplar · Class 12 · Maths
Chapter 9: Differential Equations
Practice each question, then open the answer or worked solution.
Questions
38 questionsQ12Written answer
If y(t) is a solution of and y (0) = – 1, then show that y (1) = -1/2.
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Q13Written answer
Form the differential equation having y = (sin–1x)2 + A cos–1x + B, where A and B are arbitrary constants, as its general solution.
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Q14Written answer
Form the differential equation of all circles which pass through origin and whose centres lie on y-axis.
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The equation of circles which pass through the origin and whose centre lies on the y-axis is given by,
(x – 0)2 + (y – a)2 = a2, where (0, a) is the centre
x2 + y2 + a2 – 2ay = a2
x2 + y2 – 2ay = 0 ……… (i)
Differentiating both sides w.r.t. x, we get
Q15Written answer
Find the equation of a curve passing through origin and satisfying the differential equation
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Given equation,
Q16Written answer
Solve:
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Given equation,
Q17Written answer
Find the general solution of the differential equation
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Given differential equation,
Thus, the above is the required solution of the given differential equation.
Q18Written answer
Find the general solution of y2dx + (x2 – xy + y2) dy = 0.
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Given equation, y2dx + (x2 – xy + y2) dy = 0
Q19Written answer
Solve : (x + y) (dx – dy) = dx + dy. [Hint: Substitute x + y = z after separating dx and dy]
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Given differential equation, (x + y) (dx – dy) = dx + dy
(x + y) dx – (x – y) dy = dx + dy
– (x + y) dy – dy = dx – (x + y) dx
– (x + y + 1) dy = – (x + y – 1) dx
Q20Written answer
Solve : 2 (y + 3) – xy dy/dx = 0, given that y(1) = -2.
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Given differential equation, 2 (y + 3) – xy dy/dx = 0
