62.29.1 problem Ex 1

Internal problem ID [12952]
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
Date solved : Tuesday, January 28, 2025 at 04:45:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=\cos \left (x \right )-{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=cos(x)-exp(2*x),y(x), singsol=all)
 

\[ y = \left (c_{1} +x +1\right ) {\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_{2} +\frac {\cos \left (x \right )}{10}-\frac {\sin \left (x \right )}{10} \]

✓ Solution by Mathematica

Time used: 0.240 (sec). Leaf size: 70

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==Cos[x]-Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\int _1^x\left (1-e^{-2 K[1]} \cos (K[1])\right )dK[1]+e^x \int _1^xe^{-3 K[2]} \left (\cos (K[2])-e^{2 K[2]}\right )dK[2]+c_2 e^x+c_1\right ) \]