Differential Equation questions
503 published questions with worked solutions.
- The differential equation of the family of curves, x^2=4b(y+b), b R, is :
- If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation, 2x^2dy=(2xy+y^2)dx, then f (...
- Suppose the solution of the differential equation dy dx = (2 + )x - y + 2 x - 2 y - ( - 4 ) represents a circle passing through...
- If the solution y(x) of the given differential equation (eʸ + 1)cos x dx + eʸ sin x dy = 0 passes through the point ( 2, 0 ),...
- Let y = y(x) be the solution of the differential equation, 2+ x y+1 dy dx =- x, y > 0, y(0) = 1. If y( ) = a and dy dx at x = is...
- The solution curve of differential equation, (1+e^ -x )(1+y^2) dy dx =y^2, which passes through the point (0, 1) is-
- Let f(x) be a positive function such that the area bounded by y = f(x), y = 0 from x = 0 to x = a > 0 is e⁻ᵃ + 4a² + a − 1. Then...
- Let y = y(x) be the solution curve of the differential equation sec y dy dx + 2x sin y = x³ cos y, y(1) = 0. Then y(√3) is equal...
- Let α|x| = |y|e^ xy − β , α, β ∈ N be the solution of the differential equation x dy − y dx + xy(x dy + y dx) = 0, y(1) = 2. Then...
- Let y = y(x) be the solution of the differential equation, xy'-y=x^2(x x+ x), x > 0. if y( ) = , then y'' ( 2 )+y ( 2 ) is equal...
- The solution of the differential equation dy dx - y+3x _e(y+3x) +3=0 is : (where C is a constant of integration.)
- If y = y(x) is the solution of the differential equation 5+e^x 2+y dy dx +e^x=0 satisfying y(0) = 1,then a value of y( _e13) is :
- Let y = y(x) be the solution of the differential equation x dy dx +2y x= 2x, x (0, 2 ). If y( /3) = 0, then y( /4) is equal to :
- The general solution of the differential equation 1+x^2+y^2+x^2y^2 +xy dy dx =0 is (where C is a constant of integration) :
- If y= ( 2x -1 ) cosec x is the solution of the differential equation, dy dx +p(x)y= 2 cosec x, 0 < x < 2 , then the function p(x)...
- Let x = x(y) be the solution of the differential equation 2y^2 dx dy - 2xy + x^2 = 0, y > 1, x(e) = e. Then x(e²) is equal to:
- Let y = y(x) be the solution curve of the differential equation (1 + sin x) dy dx + (y + 1)cos x = 0, y(0) = 0. If the curve y =...
- Let y = y(x) be the solution of the differential equation dy dx = (1+x+x^2)(1-y+y^2), y(0) = 12. Then (2y(1) − 1) is equal to:
- Let y=y(x) be the solution of the differential equation dy dx + ( 6x^2+(3x^2+2x^3+4)e^ -2x (x^3+2)(2+e^ -2x ) )y = 2+e^ -2x ,...
- Let y=y(x) be the solution of the differential equation ( x)^ 1/2 dy=( ^3x-( x)^ 3/2 y)dx, 0<x< 2, y ( 4 )= 6 2 5. If y ( 3 )= 45...
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