83.12.1 problem 1

Internal problem ID [19173]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (D) at page 37
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:10:52 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{4 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=exp(4*x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{2} +{\mathrm e}^{3 x} c_{1} +\frac {{\mathrm e}^{4 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{2 x} \left (e^{2 x}+2 c_2 e^x+2 c_1\right ) \]