Higher mathematics
Differential equations
Initial-value problems for common first-order equations.
Higher mathematics
Initial value problem y′ = ky
y(x) = y₀eᵏ⁽ˣ⁻ˣ⁰⁾→Higher mathematicsInitial value problem y′ + ay = b
y = b/a + (y₀−b/a)e⁻ᵃ⁽ˣ⁻ˣ⁰⁾→Higher mathematicsExponential decay
y(t) = y₀e⁻ᵏᵗ→Higher mathematicsLogistic growth equation
y = K / (1 + ((K−y₀)/y₀)e⁻ʳᵗ)→Higher mathematicsDifferential equation auto-parse
Differential equation auto-parse: calculated from the entered values→Higher mathematicsEquation y′ = f(x)
y = ∫f(x)dx + C→Higher mathematicsEquation y′ = ky
y = Ceᵏˣ→Higher mathematicsLinear homogeneous first-order ODE
y′ + ay = 0→Higher mathematicsLinear ODE with constant coefficients
y′ + ay = b→Higher mathematicsGeneral linear first-order ODE
y′ + p(x)y = q(x)→Higher mathematicsSeparable first-order ODE
y′ = g(x)h(y)→Higher mathematicsBernoulli differential equation
y′ + p(x)y = q(x)yⁿ→Higher mathematicsHomogeneous first-order ODE
y′ = F(y/x)→Higher mathematicsExact differential equation
M(x,y)dx + N(x,y)dy = 0→Higher mathematicsRiccati differential equation
y′ = a(x)y² + b(x)y + c(x)→Higher mathematicsSecond-order linear ODE
y″ + ay′ + by = c→Higher mathematicsSystem of two linear ODEs
U′ = AU→