MA 266 Exam 1 Question and answers already passed 2025/2026

MA 266 Exam 1 Question and answers
already passed 2025/2026
Linear Equation - correct answer ✔(dy/dt) + p(t)y = g(t)



Separable Equation - correct answer ✔dy/dx = h(x)*g(y)



Homogeneous Equation - correct answer ✔dy/dx = f(x,y) where f(tx,yx) = f(x,y)



Exact Equation - correct answer ✔M(x,y)dx + N(x,y)dy = 0 where ∂M/∂y = ∂N/∂x



Solution for linear equation - correct answer ✔(u(t)*y)' = u(t)*g(t), where u(t) = exp( ∫p(t)dt)



Solution for separable equation - correct answer ✔∫ (1/g(y))dy = ∫ h(x) dx



Solution for homogeneous equation - correct answer ✔Let v=y/x

Hence y' = xv' + v

Hence xv' + v = f(x,y) with v=y/x



Bernoulli's Equation - correct answer ✔y' + p(x)*y g(x)*y^n

u(t) = y^(1-n)



Euler Method - correct answer ✔t[n] = t[n-1] + h

y[n] = y[n-1] +h*f(t[n-1],y[n-1])