62.25.1 problem Ex 1

Internal problem ID [12933]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 48. Page 103
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:44:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (-x+c_2 e^x-1+c_1\right ) \]