74.15.49 problem 52

Internal problem ID [16488]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 52
Date solved : Tuesday, January 28, 2025 at 09:09:19 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 30

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

\[ y(x)\to \frac {c_2 x^2}{2}-\frac {c_1}{2 x^2}+2 \log (x)+c_3 \]