73.8.40 problem 13.6 (f)

Internal problem ID [15248]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.6 (f)
Date solved : Tuesday, January 28, 2025 at 07:50:52 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=1\\ y^{\prime \prime }\left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 18

dsolve([x*diff(y(x),x$3)+2*diff(y(x),x$2)=6*x,y(1) = 2, D(y)(1) = 1, (D@@2)(y)(1) = 4],y(x), singsol=all)
 

\[ y = \frac {x^{3}}{3}-2 \ln \left (x \right )+2 x -\frac {1}{3} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 21

DSolve[{x*D[y[x],{x,3}]+2*D[y[x],{x,2}]==6*x,{y[1]==2,Derivative[1][y][1]==1,Derivative[2][y][1]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \left (x^3+6 x-6 \log (x)-1\right ) \]