Internal problem ID [4106]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.11, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }-2 \,{\mathrm e}^{2 x} \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-3*diff(y(x),x)=2*exp(2*x)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{3 x}}{3}-\frac {\cos \relax (x ) {\mathrm e}^{2 x}}{5}-\frac {3 \sin \relax (x ) {\mathrm e}^{2 x}}{5}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.282 (sec). Leaf size: 33
DSolve[y''[x]-3*y'[x]==2*Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{15} e^{2 x} \left (-9 \sin (x)-3 \cos (x)+5 c_1 e^x\right )+c_2 \\ \end{align*}