Differential Equation questions
503 published questions with worked solutions.
- Let y = y(x) be the solution curve of the differential equation (1 + x^2)dy + (y - ^ -1 x)dx = 0, y(0) = 1. Then the value of...
- Let y = y(x) be the solution of the differential equation x dy dx - 2y = 2 + 3 x, x (- 2 , 2 ), y(0) = - 7 4 . Then y ( 6 ) is...
- Let the solution curve of the differential equation xdy - ydx = x^2+y^2 ,dx, x > 0, y(1) = 0, be y = y(x). Then y(3) is equal to
- If y=y(x) satisfies the differential equation 16 ( x+9 x ) (4+ 9+ x ) y , dy = (1+2 y)dx, x>0 and y(256) = 2 , y(49) = , then 2...
- Let y=y(x) be the solution of the differential equation x^4 dy + (4x^3y + 2 x)dx = 0, x>0, y ( 2 )=0. Then ^4 y ( 3 ) is equal to...
- If the solution curve y = f(x) of the differential equation (x^2-4)y' - 2xy + 2x(4-x^2)^2 = 0, x > 2, passes through the point...
- Let y=y(x) be the solution of the differential equation x dy dx - 2y = x^3(2-x^3) ^2 y, x 0. If y(2)=0, then (y(1)) is equal to
- Let y=y(x) be the solution of the differential equation x dy dx -y=x^2 x, x (0, ). If y ( 2 )= 2 , then 6y ( 6 )-8y ( 4 ) is...
- If x = f(y) is the solution of the differential equation (1+y^2) + (x - 2e^ ^ -1 y ) dy dx = 0, y (- 2 , 2 ) With f(0) = 1, then...
- Let y = f(x) be the solution of the differential equation dy dx + xy x^2-1 = x^6+4x 1-x^2 , -1 < x < 1 such that f(0) = 0. If 6 _...
- Let x = x(y) be the solution of the differential equation y = (x - y dx dy ) ( x y ), y > 0 and x(1) = 2 . Then (x(2)) is equal...
- Let a curve y = f(x) pass through the points (0, 5) and ( _e2, k). If the curve satisfies the differential equation 2(3+y)e^ 2x...
- Let y = y(x) be the solution of the differential equation (xy - 5x^2 1+x^2 )dx + (1+x^2)dy = 0, y(0) = 0. Then y( 3 ) is equal to
- Let f : (0, ) R be a function which is differentiable at all points of its domain and satisfies the condition x^2f'(x) = 2xf(x) +...
- Let y = y(x) be the solution of the differential equation 2 x dy dx = 2x - 4y x, x (0, 2 ). If y ( 3 )=0, then y' ( 4 )+y ( 4 )...
- If y = y(x) is the solution of the differential equation, 4-x^2 dy dx = ( ( ^ -1 ( x 2 ) )^2-y ) ^ -1 ( x 2 ), -2 x 2, y(2)= (...
- Let y = y(x) be the solution of the differential equation x( _e( x))^2 dy + ( x - 3y x _e( x))dx = 0, x (0, 2 ). If y ( 4 ) = -1...
- If for the solution curve y = f(x) of the differential equation dy dx +( x)y= 2+ x (1+2 x)^2 , x ( - 2 , 2 ), f ( 3 )= 3 10 ,...
- Let y = y(x) be the solution of the differential equation dy dx + 2y ^2 x = 2 ^2 x + 3 x ^2 x such that y(0) = 5 4 . Then 12 (y (...
- Let y = y(x) be the solution of the differential equation dy dx + 3( ^2 x)y + 3y = ^2 x, y(0) = 1 3 + e^3. Then y ( 4 ) is equal...
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