Internal problem ID [13379]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.1 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }={\mathrm e}^{\frac {x}{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)+3*diff(y(x),x)=exp(x/2),y(x), singsol=all)
\[ y = -\frac {c_{1} {\mathrm e}^{-3 x}}{3}+\frac {4 \,{\mathrm e}^{\frac {x}{2}}}{7}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 30
DSolve[y''[x]+3*y'[x]==30*Exp[x/2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {120 e^{x/2}}{7}-\frac {1}{3} c_1 e^{-3 x}+c_2 \]