Differential Equations for University Entrance Exams

Succeeding in highly competitive university entrance exams requires a deep, intuitive understanding of calculus and mathematical modeling. This course breaks down complex mathematical theories into clear, structured written lessons designed to help you build solid problem-solving skills. You will transition from basic calculus to solving advanced first-order and higher-order differential equations with confidence through detailed written explanations, step-by-step derivations, and solved practice problems. What you'll learn: Learn foundational definitions, order, degree, and linearity of differential equations; Solve first-order ordinary differential equations using separable, homogeneous, and exact methods; Apply integrating factors to solve linear differential equations systematically; Master higher-order linear differential equations with constant coefficients; Analyze solutions using Wronskians and find particular integrals for various functions; Practice solving standard partial differential equations commonly featured in competitive exams; Explore modern numerical techniques including Euler's method for approximating solutions. The course begins with essential terminology and core definitions before progressing systematically through first-order equations, higher-order linear equations, and introductory partial differential equations, featuring rigorous written practice problems along the way. This course is designed for undergraduate students, mathematics majors, and aspirants preparing for competitive university entrance exams, with a basic understanding of introductory calculus recommended. Start reading today to master differential equations and boost your exam readiness.