Differential Equation questions
503 published questions with worked solutions.
- If the solution curve y = y(x) of the differential equation y^ 2 dx + (x^ 2 − xy + y^ 2 )dy = 0, which passes through the point...
- Let the solution curve y = f(x) of the differential equation dy/dx + xy/(x^ 2 - 1) = (x^ 4 + 2x)/ 1 - x^ 2 , x (−1, 1) pass...
- Suppose y = y(x) be the solution curve to the differential equation dy/dx − y = 2 - e^ -x such that _ x y(x) is finite. If a and...
- If dy/dx + 2y tan x = sin x, 0 < x < /2 and y( /3) = 0, then the maximum value of y(x) is :
- If the solution of the differential equation dy/dx + e^ x (x^ 2 - 2)y = (x^ 2 - 2x)(x^ 2 - 2)e^ 2x satisfies y(0) = 0, then the...
- Let the solution curve y = y(x) of the differential equation (4 + x^ 2 )dy - 2x(x^ 2 + 3y + 4)dx = 0 pass through the origin....
- Let S = (0, 2 ) - /2, 3 /4, 3 /2, 7 /4 . Let y = y(x), x S, be the solution curve of the differential equation dy/dx = 1/(1 + sin...
- If dy dx = 2^xy+2^y.2^x 2^x+2^ x+y _e2 , y(0) = 0, then for y = 1, the value of x lies in the interval :
- Let x= (x^ y^ ) be the solution of differential equation 2x^2ydy-(1-xy^2)dx=0, x > 0, y(2) = _e2 . Then + - equals :
- If y = y(x) is the solution curve of the differential equation dt dx +y x=x x, 0 x 3 , y(0) = 1, then y ( 6 ) is equal to
- The area enclosed by the closed curve C given by the differential equation dy dx + x+a y-2 =0, y(1) = 0 is 4 . Let P and Q be the...
- Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x R , where f'(x) denotes d f(x) dx and g(x) is a given non-constant differentiable...
- If y(x) satisfies the differential equation y' - y x = 2x x and y(0) = 0, then
- A curve passes through the point (1, 6 ). Let the slope of the curve at each point (x, y) be y x + ( y x ), x > 0. Then the...
- Let y(x) be a solution of the differential equation (1+e^x)y'+ye^x=1. If y(0)=2, then which of the following statements is (are)...
- Consider the family of all circles whose centers lie on the straight line y=x. If this family of circles is represented by the...
- A solution curve of the differential equation (x^2+xy+4x+2y+4) dy dx -y^2=0, x>0, passes through the point (1,3). Then the...
- If y=y(x) satisfies the differential equation 8 x ( 9+ x )dy= ( 4+ 9+ x )^ -1 dx, x>0 and y(0)= 7 , then y(256)=
- Let f: R R be a differentiable function with f(0)=0. If y=f(x) satisfies the differential equation dy dx =(2+5y)(5y-2), then the...
- What are the degree and order respectively of the differential equation satisfying e^ y 1-x^2 +x 1-y^2 =ce^x (where c>0, |x|<1,...
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