DIFFERENTIAL EQUATIONS STUDY GUIDE . QUESTIONS AND CORRECT ANSWERS 2025

DIFFERENTIAL EQUATIONS STUDY GUIDE . QUESTIONS
AND CORRECT ANSWERS 2025


QUESTION: 1st order linear ODE - ANSWER-Use Integrating factor (dy/dx + p(x)y = f(x))




QUESTION: 1st order nonlinear ODE check first - ANSWER-separable (dy/dx = 2x/(1+y)




QUESTION: 1st order nonlinear ODE check second - ANSWER-exact (My dx + Nx dy = 0)




QUESTION: 1st order nonlinear ODE check third - ANSWER-homogeneous (y/x ratio and u=y/x)




QUESTION: 1st order nonlinear ODE check fourth - ANSWER-Bernoulli's (dy/dx + p(x)y = f(x) y^n)




QUESTION: (2x - 1)dx + (3y+7)dy = 0 - ANSWER-separable, exact




f(x,y) = x^2 - x + 3/2y^2 + 7y + c




QUESTION: (2x + y)dx - (x+6y)dy = 0 - ANSWER-homogeneous

, QUESTION: (2xy^2 - 3)dx + (2x^2(y) + 4)dy = 0 - ANSWER-exact




f(x,y) = (x^2)(y^2)-3x + 4y + c




QUESTION: (x^3 + y^3)dx + (3xy^2)dy = 0 - ANSWER-exact




1/4x^4 + xy^3 = c




QUESTION: (3x^2(y) + e^y)dx + (x^3 + xe^y - 2y)dy = 0 - ANSWER-exact




f(x,y) = x^3(y) + xe^y -y^2 + c




QUESTION: (5y - 2x)dy - (2y)dx = 0 - ANSWER-exact




5/2y^2 - 2xy = c




QUESTION: (x^2 + y^2)dx + (x^2 - xy)dy = 0 - ANSWER-homogeneous




(-y/x)-2ln((y/x)+1) = -ln(x) + c