Internal problem ID [15246]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 476.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+3*diff(y(x),x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-3 x} \left (-3 c_{2} {\mathrm e}^{3 x}+c_{1} -\frac {3 \,{\mathrm e}^{4 x}}{4}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 26
DSolve[y''[x]+3*y'[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{4}-\frac {1}{3} c_1 e^{-3 x}+c_2 \]