Consider the differential equation y''+3y'-4y=e^ 2x

MATHEMATICS · Multi-part · IB Diploma Programme · Mathematics: Applications and Interpretation · Calculus · Calculus

Problem

Consider the differential equation y′′+3y′−4y=e2x.y''+3y'-4y=e^{2x}. A candidate particular solution is yp(x)=Ae2xy_{p}(x)=A e^{2x}, where AA is a constant coefficient to be determined. (a) Calculate yp′(x)y_{p}'(x) and yp′′(x)y_{p}''(x). (b) Substitute ypy_{p}, yp′y_{p}', and yp′′y_{p}'' into the differential equation and determine the value of AA that satisfies the equation for all real xx. (c) Write the general solution y(x)y(x) of the differential equation. (d) Verify by direct substitution that the general solution found in part (c) satisfies the original differential equation.

Related theory

Browse the problem library