83.15.4 problem 4

Internal problem ID [19189]
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 (G) at page 45
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:11:52 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 41

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

\[ y \left (x \right ) = \left (-c_{1} x -c_{1} -c_{2} \right ) {\mathrm e}^{-x}+\frac {x^{3}}{3}-\frac {3 x^{2}}{2}+4 x +c_3 +\frac {{\mathrm e}^{2 x}}{18} \]

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 50

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

\[ y(x)\to \frac {x^3}{3}-\frac {3 x^2}{2}+4 x+\frac {e^{2 x}}{18}-e^{-x} (c_2 (x+1)+c_1)+c_3 \]