Internal problem ID [10262]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary.
Page 117
Problem number: Ex 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }+6 y-\cos \relax (x )+{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=cos(x)-exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} c_{2}+{\mathrm e}^{3 x} c_{1}+\frac {\left (10 x +10\right ) {\mathrm e}^{2 x}}{10}+\frac {\cos \relax (x )}{10}-\frac {\sin \relax (x )}{10} \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 34
DSolve[y''[x]-5*y'[x]+6*y[x]==Cos[x]-Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{10} \left (-\sin (x)+\cos (x)+10 e^{2 x} \left (x+c_2 e^x+1+c_1\right )\right ) \\ \end{align*}