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प्रश्न
Form the differential equation representing the family of curves given by (x – a)2 + 2y2 = a2, where a is an arbitrary constant.
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उत्तर
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संबंधित प्रश्न
Which of the following differential equations has y = c1 ex + c2 e–x as the general solution?
(A) `(d^2y)/(dx^2) + y = 0`
(B) `(d^2y)/(dx^2) - y = 0`
(C) `(d^2y)/(dx^2) + 1 = 0`
(D) `(d^2y)/(dx^2) - 1 = 0`
Which of the following differential equation has y = x as one of its particular solution?
A. `(d^2y)/(dx^2) - x^2 (dy)/(dx) + xy = x`
B. `(d^2y)/(dx^2) + x dy/dx + xy = x`
C. `(d^2y)/(dx^2) - x^2 dy/dx + xy = 0`
D. `(d^2y)/(dx^2) + x dy/dx + xy = 0`
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\[\frac{dy}{dx} - y = \cos 2x\]
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\[x\frac{dy}{dx} + 2y = x^2 \log x\]
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