Ordinary differential equations, their order and degree; formation of differential equations; solution of differential equations by the method of separation of variables; solution of homogeneous and linear differential equations of the first order.
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Q1 · Differential Equations · EASY
The order and degree of the differential equation (1 + (dy/dx)²)^(3/2) = k(d²y/dx²) are respectively:
Q2 · Differential Equations · EASY
The differential equation representing the family of curves y = A cos(x) + B sin(x), where A and B are arbitrary constants, is:
Q3 · Differential Equations · MEDIUM
The solution of the differential equation dy/dx = (x + y)/(x - y) is:
Q4 · Differential Equations · MEDIUM
The general solution of the differential equation (x + 2y³)dy = y dx is:
Q5 · Differential Equations · HARD
If y = y(x) satisfies the differential equation (x cos(x) + sin(x))dy = y sin(x) dx and y(π) = π, then the value of y(π/2) is: