Differential Equation questions
503 published questions with worked solutions.
- Let y=y(x) be the solution of the differential equation x ( yx )dy= (y ( yx )-x )dx, y(1)=π/2 and let = ( y(e^ 12 ) e^ 12 ). Then...
- Let y=y(x) be the solution of the differential equation (x^2-x x^2-1 )dy+(y(x- x^2-1 )-x)dx=0, x≥1. If y(1)=1, then the greatest...
- Let y = y(x) be the solution of the differential equation x 1-x^2 ,dy+ (y 1-x^2 -x ^ -1 x )dx=0, x ∈ (0, 1), _ x 1^- y(x)=1. Then...
- The solution curve, of the differential equation 2y dy dx + 3 = 5 dy dx , passing through the point (0, 1) is a conic, whose...
- The solution of the differential equation (x² + y²)dx − 5xy dy = 0, y(1) = 0 is :
- If y = y(x) is the solution curve of the differential equation (x² – 4)dy – (y² – 3y)dx = 0, x > 2, y(4) = 3/2 and the slope of...
- If the solution curve, of the differential equation dy dx = x + y - 2 x - y passing through the point (2, 1) is ^ -1 ( y-1 x-1 )...
- Let x = x(t) and y = y(t) be solutions of the differential equations dx dt + ax = 0 and dy dt + by = 0 respectively, a, b ∈ R....
- If the solution of the differential equation (2x + 3y – 2)dx + (4x + 6y – 7)dy = 0, y(0) = 3, is αx + βy + 3log_e|2x + 3y – γ| =...
- If ( yx ) = _e|x| + 2 is the solution of the differential equation x ( yx ) dy dx = y ( yx ) + x and y(1) = 3, then α² is equal to
- A function y = f(x) satisfies f(x) sin 2x + sin x – (1 + cos²x) f ′(x) = 0 with condition f(0) = 0. Then, f(π/2) is equal to-
- If the solution curve y = y(x) of the differential equation (1 + y²)(1 + log_e x)dx + x dy = 0, x > 0 passes through the point...
- Let Y = Y(X) be a curve lying in the first quadrant such that the area enclosed by the line Y − y = Y′(x)(X − x) and the...
- Let y = y(x) be the solution of the differential equation sec x dy + 2(1 – x)tan x + x(2 – x) dx = 0 such that y(0) = 2. Then...
- Let y = y(x) be the solution of the differential equation (1 - x^2)dy = [xy + (x^3 + 2) 3(1 - x^2) ]dx, −1 < x < 1, y(0) = 0. If...
- The temperature T(t) of a body at time t = 0 is 160°F and it decreases continuously as per the differential equation dT/dt = −K(T...
- Let y = y(x) be the solution of the differential equation sec²x dx + (e²ʸ tan²x + tan x)dy = 0, 0 < x < π/2, y(π/4) = 0. If...
- The solution curve of the differential equation y dx dy = x( _ex - _ey + 1), x > 0, y > 0 passing through the point (e, 1) is
- Let y = y(x) be the solution of the differential equation dy dx = ( x) + y x( x - x x) , x ∈ (0, π/2) satisfying the condition...
- If y = y (x) is the solution curve of the differential equation x^2dy+ (y- 1 x )dx=0, x > 0 and y(1) = 1, then y ( 1 2 ) is equal...
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