83.16.5 problem 5

Internal problem ID [19194]
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 (H) at page 47
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:13:00 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (1+x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 34

dsolve(diff(y(x),x$3)-7*diff(y(x),x)-6*y(x)=exp(2*x)*(1+x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\left (\left (x +\frac {17}{12}\right ) {\mathrm e}^{4 x}-12 c_{2} {\mathrm e}^{x}-12 c_3 \,{\mathrm e}^{5 x}-12 c_{1} \right ) {\mathrm e}^{-2 x}}{12} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 44

DSolve[D[y[x],{x,3}]-7*D[y[x],x]-6*y[x]==Exp[2*x]*(1+x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{144} e^{2 x} (12 x+17)+c_1 e^{-2 x}+c_2 e^{-x}+c_3 e^{3 x} \]