Consider the family of all circles whose centres lie on the straight line y = x . If this…
Mathematics · JEE Advanced · NTA Exams — Differential Equations
Consider the family of all circles whose centres lie on the straight line y = x. If this family of circles is represented by the differential equation Py′′ + Qy′ + 1 = 0, where P, Q are functions of x, y and y′ \(\left(\text { here } y^{\prime}=\frac{d y}{d x}, y^{\prime \prime}=\frac{d^{2} y}{d x^{2}}\right),\) then which of the following statements is (are) true?
- P = y + x
- P = y – x
- P + Q = 1 – x + y + y′ + (y′)2
- P – Q = x + y – y′ – (y′)2
Answer
(D) P – Q = x + y – y ′ – ( y ′ ) 2
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- A Explanation:tion of the differential equation ( d y d x )^ 2 -x d y d x +y=0 is:
- The curve for which the sum of the lengths of the tangent and subtangent at any of its point is proportional…
- A solution curve of the differential equation (x^ 2 +x y+4 x+2 y+4 ) d y d x -y^ 2 =0, x>0 passes through the…
- If y ( t ) is a solution of and y (0) = –1, then y (1) is equal to
- The Explanation:tion of the differential equation d ^ 2 y dx ^ 2 = sin3x + e x + x 2 when y’(0) = 1 and y (0)…
- Explanation:tion of the differential equation (e^ x^ 2 +e^ y^ 2 ) y d y d x + e ^ x ^ 2 ( xy ^ 2 - x ) = 0, is
- The differential equation of all the ellipses centred at the origin and having their axes as co-ordinate axes…
- The Explanation:tion of p^ 2 +(2 y x) p=y^ 2 where p= d y d x is
More Differential Equations questions · Browse all practice questions