15.11.14 problem 14

Internal problem ID [3124]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 14
Date solved : Monday, January 27, 2025 at 07:21:14 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

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

\[ y = -\frac {65 x^{2}}{64}-\frac {x^{3}}{48}-\frac {x^{4}}{48}+\frac {{\mathrm e}^{4 x} c_{1}}{16}+c_2 x +c_3 \]

✓ Solution by Mathematica

Time used: 0.174 (sec). Leaf size: 41

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

\[ y(x)\to \frac {1}{192} \left (-4 x^4-4 x^3-195 x^2+12 c_1 e^{4 x}\right )+c_3 x+c_2 \]