82.29.1 problem Ex. 1

Internal problem ID [18883]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 76
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:33:22 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

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

\[ y \left (x \right ) = \frac {x^{3}}{6}-\frac {3 x^{2}}{4}-c_{2} {\mathrm e}^{-x}+\frac {{\mathrm e}^{-2 x} c_{1}}{2}+\frac {7 x}{4}+c_3 \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 47

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

\[ y(x)\to \frac {x^3}{6}-\frac {3 x^2}{4}+\frac {7 x}{4}-\frac {1}{2} c_1 e^{-2 x}-c_2 e^{-x}+c_3 \]