Differential Equation questions
503 published questions with worked solutions.
- Let us consider a curve, y = f(x) passing through the point (–2, 2) and the slope of the tangent to the curve at any point (x,...
- A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rectum is the...
- If the solution curve of the differential equation (2x-10y^3)dy+ydx=0, passes through the points (0, 1) and (2, ), then is a root...
- If dy dx = 2^ x+y -2^x 2^y , y(0) = 1, then y(1) is equal to :
- If the curve, y = y(x) represented by the solution of the differential equation (2xy^2-y)dx+xdy=0, passes through the...
- If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is x^2-4x+y+8 x-2 , then this curve...
- Let y = y (x) be the solution of the differential equation xdy = (y + x^3 x)dx with y( )=0, then y ( 2 ) is equal to :
- Let a curve y = f(x) pass through the point (2, ( _e2)^2) and have slope 2y x _ex for all positive real value of x. Then the...
- Let y = y(x) be solution of the differential equation dy dx =1+xe^ y-x , - 2<x< 2, y(0)=0, then, the minimum value of y(x), x (-...
- Let y = y(x) be solution of the following differential equation e^y dy dx -2e^y x+ x ^2x=0, y ( 2 )=0 If y(0) = _e( + e^ -2 ),...
- Let y(x) be the solution of the differential equation 2x^2dy+(e^y-2x)dx=0, x > 0. If y(e) = 1, then y(1) is equal to:
- Let y = y(x) be a solution curve of the differential equation (y + 1) ^2x dx + tan x dy + y dx = 0, x (0, 2 ). If _ x 0^+...
- The difference between degree and order of a differential equation that represents the family of curves given by y^2=a (x+ a 2 ),...
- If y = y(x) is the solution of the equation e^ y y dy dx +e^ y x= x, y(0) = 0: then 1+y ( 6 )+ 3 2 y ( 3 )+ 1 2 y ( 4 ) is equal...
- If x = x(y) is the solution of the differential equation y dx/dy = 2x + y^ 3 (y + 1)e^ y , x(1) = 0 ; then x(e) is equal to
- The slope of normal at any point (x, y), x > 0, y > 0 on the curve y = y(x) is given by x^ 2 /(xy - x^ 2 y^ 2 - 1). If the curve...
- Let a smooth curve y = f(x) be such that the slope of the tangent at any point (x, y) on it is directly proportional to (−y)/x....
- The general solution of the differential equation (x - y^ 2 )dx + y(5x + y^ 2 )dy = 0 is :
- If y = y(x) is the solution of the difference equation 2x^ 2 dy/dx − 2xy + 3y^ 2 = 0 such that y( ) = /3, then y(1) is equal to
- Let y = y(x) be the solution of the differential equation (x + 1)y' - y = e^ 3x (x + 1)^ 2 , with y(0) = 1/3. Then, the point x =...
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