MA 266 Exam 1 Questions with complete solution 2025/2026

MA 266 Exam 1 Questions with
complete solution 2025/2026
Linear Differential Equation - correct answer ✔The dependent var and its derivatives appear in additive
combos of their first power



Separable DE - correct answer ✔Separable can be written as: P(y) dy/dx = q(x) and separated as P(y)dy
= q(x)dx



1st order linear DE - correct answer ✔standard form: y' + p(x)y = q(x)

Integrating factor method:

-find I(x) = e^int(p(x)dx)

-solve: (I(x)y)' = I(x)q(x)



Mixing problem - correct answer ✔C(t) = A(t)/V(t)

dV/dt = r1-r2

dA/dt = C1r1-C2r2

dA/dt + r2A/V = C1r1 (1st order linear)



Exact Equations - correct answer ✔M(x,y) +N(x,y) dy/dx = 0 (2 distinct funcs, =0 and "+")

Ix = M, Iy = N, if exact, My = Nx

I(x,y) = C

integrate Mdx, to get I, have +h(y) instead of +C, Iy = N to find h(y)



Bernoulli DE - correct answer ✔Form: y' +p(x)y = q(x)y^n (linear with y^n)

Solve: (1) divide by y^n, use v=y^1-n, v' = (1-n)(y^-n)y'