15.4 problem 22.1 (d)

Internal problem ID [13699]

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: 25

dsolve(diff(y(x),x$2)+3*diff(y(x),x)=exp(x/2),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {{\mathrm e}^{-3 x} \left (-3 c_{2} {\mathrm e}^{3 x}+c_{1} -\frac {12 \,{\mathrm e}^{\frac {7 x}{2}}}{7}\right )}{3} \]

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]
 

\[ y(x)\to \frac {120 e^{x/2}}{7}-\frac {1}{3} c_1 e^{-3 x}+c_2 \]