Differential Equation questions
503 published questions with worked solutions.
- Let y = y(x) be the solution of the differential equation dy/dx + ( 2y )/(2 ^ 4 x - 2x) = x e^ ^ -1 ( 2 cot 2x) , 0 < x < /2 with...
- The solution of the differential equation dy dx = (y-x)+1 is
- The differential equation of the system of circles touching the y-axis at the origin is
- Consider the following in respect of the differential equation : d^2y dx^2 +2 ( dy dx )^2+9y=x 1. The degree of the differential...
- What is the general solution of the differential equation dy dx + x y =0?
- Let y(x) be the solution of the differential equation x^2 dy dx + xy = x^2 + y^2, x > 1 e , satisfying y(1) = 0. Then the value...
- Let y = y(x) be a solution of the differential equation (xcosx)dy + (xysinx + ycosx – 1)dx = 0, 0 < x < 2 . If 3 y ( 3 )= 3, then...
- Let the solution curve x = x(y), 0<y< 2 , of the differential equation ( _e( y))^2 ydx-(1+3x _e( y)) ydy=0 satisfy x ( 3 )= 1 2...
- If the solution curve of the differential equation (y – 2 _ex)dx + (x _ex^2)dy = 0, x > 1 passes through the points (e, 4 3 ) and...
- Let the tangent at any point P on a curve passing through the points (1, 1) and ( 1 10 ,100 ), intersect positive x-axis and...
- The slope of tangent at any point (x, y) on a curve y = y(x) is x^2+y^2 2xy , x > 0. If y(2) = 0, then a value of y(8) is
- Let y = y(x) be a solution curve of the differential equation (1-x^2y^2)dx=ydx+xdy. If the line x = 1 intersects the curve y =...
- Let y = y(x), y > 0, be a solution curve of the differential equation (1+x^2)dy=y(x-y)dx. If y(0) = 1 and y(2 2)= , then
- Let y = y_1(x) and y = y_2(x) be the solution curves of the differential equation dy dx = y + 7 with initial conditions y_1(0) =...
- Let x = x(y) be the solution of the differential equation 2(y+2) _e(y+2)dx+(x+4-2 _e(y+2))dy=0, y > –1 with x(e^4-2) = 1. Then...
- Let y = y(t) be a solution of the differential equation dy dt + y= e^ - t where > 0, > 0 and > 0. Then _ x y(t)
- Let y = y(x) be the solution curve of the differential equation dy dx = y x (1+xy^2(1+ _ex)), x > 0, y(1) = 3. Then y^2(x) 9 is...
- Let y = y(x) be the solution of the differential equation x _ex dy dx +y=x^2 _ex, (x > 1). If y(2) = 2, then y(e) is equal to
- Let y = f(x) be the solution of the differential equation y(x+1)dx – x^2dy = 0, y(1) = e. Then _ x 0 f(x) is equal to
- The solution of the differential equation dy dx =- ( x^2+3y^2 3x^2+y^2 ), y(1)=0 is
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