Differential Equations Visual Explorer

1. Show that each expression is a solution of the given differential equation.

(i) y = 2x² ; xy' = 2y

(ii) y = aeˣ + be⁻ˣ ; y'' - y = 0

2. Find value of m so that y = eᵐˣ is a solution.

(i) y' + 2y = 0

(ii) y'' - 5y' + 6y = 0

3. Find curve equation where slope is reciprocal of 4 times the ordinate, passing through (2,5).
4. Show y = e⁻ˣ + mx + n is a solution of eˣ(d²y/dx²) - 1 = 0.
5. Show y = ax + b/x is a solution of x²y'' + xy' - y = 0.
6. Show y = ae⁻³ˣ + b is a solution of d²y/dx² + 3dy/dx = 0.
7. Show the differential equation for the family of curves y² = 2a(x + a^(2/3)) is (y² - 2xyy')³ = 8(yy')⁵.
8. Show y = a cos(bx) is a solution of d²y/dx² + b²y = 0.