40.10.10 problem 19

Internal problem ID [6732]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 15. Linear equations with constant coefficients (Variation of parameters). Supplemetary problems. Page 98
Problem number : 19
Date solved : Monday, January 27, 2025 at 02:25:37 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2}+4 x +8 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+2*diff(y(x),x)=x^2+4*x+8,y(x), singsol=all)
 

\[ y = \frac {x^{2}}{4}+\frac {x^{3}}{6}-c_2 \,{\mathrm e}^{-x}+\frac {{\mathrm e}^{-2 x} c_1}{2}+\frac {11 x}{4}+c_3 \]

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 43

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]+2*D[y[x],x]==x^2+4*x+8,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} \left (2 x^3+3 x^2+33 x-6 e^{-2 x} \left (2 c_2 e^x+c_1\right )\right )+c_3 \]